2ndPaper_RStats.ipynb

{
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   "outputs": [
    {
     "name": "stderr",
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     "text": [
      "Loading required package: lme4\n",
      "\n",
      "Loading required package: Matrix\n",
      "\n",
      "\n",
      "Attaching package: ‘simr’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:lme4’:\n",
      "\n",
      "    getData\n",
      "\n",
      "\n",
      "\n",
      "Attaching package: ‘lmerTest’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:lme4’:\n",
      "\n",
      "    lmer\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    step\n",
      "\n",
      "\n",
      "\n",
      "Attaching package: ‘mice’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    filter\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    cbind, rbind\n",
      "\n",
      "\n",
      "In case you would like cite this package, cite it as:\n",
      "     Patil, I. (2018). ggstatsplot: \"ggplot2\" Based Plots with Statistical Details. CRAN.\n",
      "     Retrieved from https://cran.r-project.org/web/packages/ggstatsplot/index.html\n",
      "\n",
      "This is rstantools version 2.1.1\n",
      "\n",
      "Loading required package: ggplot2\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>155</li><li>23</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 155\n",
       "\\item 23\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 155\n",
       "2. 23\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 155  23"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t155 obs. of  23 variables:\n",
      " $ X      : int  0 1 2 3 4 5 6 7 8 9 ...\n",
      " $ NDR    : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ SUBJECT: Factor w/ 44 levels \"1\",\"2\",\"3\",\"4\",..: 1 2 3 4 5 6 7 8 9 10 ...\n",
      " $ GROUP  : Factor w/ 3 levels \"aV1-gV5\",\"gV1-aV5\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ TIMEP  : Factor w/ 4 levels \"Bsl\",\"TP0\",\"TP10\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSDA   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSDB   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSDG   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ COHA   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ COHB   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ COHG   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ V1pV5a : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ V1aV5p : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ WPLIA  : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ WPLIB  : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ WPLIG  : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSIT   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSIA   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSIB   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSIG   : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ IMCOHA : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ IMCOHB : num  1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ IMCOHG : num  1 1 1 1 1 1 1 1 1 1 ...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'aV1-gV5'</li><li>'gV1-aV5'</li><li>'Sham'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'aV1-gV5'\n",
       "\\item 'gV1-aV5'\n",
       "\\item 'Sham'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'aV1-gV5'\n",
       "2. 'gV1-aV5'\n",
       "3. 'Sham'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"aV1-gV5\" \"gV1-aV5\" \"Sham\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + GROUP * V1pV5a + (1 | SUBJECT)\n",
       "   Data: ndr\n",
       "\n",
       "REML criterion at convergence: -32.8\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.5078 -0.4791  0.0737  0.4258  3.3649 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.009015 0.09495 \n",
       " Residual             0.023856 0.15445 \n",
       "Number of obs: 111, groups:  SUBJECT, 44\n",
       "\n",
       "Fixed effects:\n",
       "                      Estimate Std. Error         df t value Pr(>|t|)    \n",
       "(Intercept)           1.042357   0.044737  76.919623  23.300  < 2e-16 ***\n",
       "TIMEPTP10            -0.116394   0.036412  71.979182  -3.197 0.002067 ** \n",
       "TIMEPTP30            -0.132475   0.035993  71.485005  -3.681 0.000448 ***\n",
       "GROUPaV1-gV5         -0.065580   0.056454  54.740978  -1.162 0.250418    \n",
       "GROUPgV1-aV5         -0.058116   0.055765  55.783929  -1.042 0.301839    \n",
       "V1pV5a                0.001443   0.018208 100.198352   0.079 0.937009    \n",
       "GROUPaV1-gV5:V1pV5a   0.004254   0.021342  98.562576   0.199 0.842422    \n",
       "GROUPgV1-aV5:V1pV5a  -0.013127   0.019334  98.822949  -0.679 0.498753    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "                 (Intr) TIMEPTP1 TIMEPTP3 GROUPV1-gV5 GROUPgV1-V5 V1pV5a\n",
       "TIMEPTP10        -0.347                                                 \n",
       "TIMEPTP30        -0.295  0.429                                          \n",
       "GROUPV1-gV5      -0.674  0.010   -0.027                                 \n",
       "GROUPgV1-V5      -0.689  0.043   -0.040    0.545                        \n",
       "V1pV5a           -0.464 -0.039   -0.085    0.390       0.396            \n",
       "GROUPV1-gV5:V1V5  0.390  0.049    0.080   -0.422      -0.337      -0.854\n",
       "GROUPgV1-V5:V1V5  0.449  0.003    0.063   -0.368      -0.442      -0.940\n",
       "                 GROUPV1-gV5:V1V5\n",
       "TIMEPTP10                        \n",
       "TIMEPTP30                        \n",
       "GROUPV1-gV5                      \n",
       "GROUPgV1-V5                      \n",
       "V1pV5a                           \n",
       "GROUPV1-gV5:V1V5                 \n",
       "GROUPgV1-V5:V1V5  0.802          "
      ]
     },
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     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 10 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.04206471</td><td> 0.13296624</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.12777705</td><td> 0.17790788</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.95701699</td><td> 1.12747445</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP10</th><td>-0.18618492</td><td>-0.04638226</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.20118259</td><td>-0.06278061</td></tr>\n",
       "\t<tr><th scope=row>GROUPaV1-gV5</th><td>-0.17302595</td><td> 0.04272109</td></tr>\n",
       "\t<tr><th scope=row>GROUPgV1-aV5</th><td>-0.16425876</td><td> 0.04876608</td></tr>\n",
       "\t<tr><th scope=row>V1pV5a</th><td>-0.03325171</td><td> 0.03619419</td></tr>\n",
       "\t<tr><th scope=row>GROUPaV1-gV5:V1pV5a</th><td>-0.03657595</td><td> 0.04489294</td></tr>\n",
       "\t<tr><th scope=row>GROUPgV1-aV5:V1pV5a</th><td>-0.05003009</td><td> 0.02373085</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 10 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.04206471 &  0.13296624\\\\\n",
       "\t.sigma &  0.12777705 &  0.17790788\\\\\n",
       "\t(Intercept) &  0.95701699 &  1.12747445\\\\\n",
       "\tTIMEPTP10 & -0.18618492 & -0.04638226\\\\\n",
       "\tTIMEPTP30 & -0.20118259 & -0.06278061\\\\\n",
       "\tGROUPaV1-gV5 & -0.17302595 &  0.04272109\\\\\n",
       "\tGROUPgV1-aV5 & -0.16425876 &  0.04876608\\\\\n",
       "\tV1pV5a & -0.03325171 &  0.03619419\\\\\n",
       "\tGROUPaV1-gV5:V1pV5a & -0.03657595 &  0.04489294\\\\\n",
       "\tGROUPgV1-aV5:V1pV5a & -0.05003009 &  0.02373085\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 10 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.04206471 |  0.13296624 |\n",
       "| .sigma |  0.12777705 |  0.17790788 |\n",
       "| (Intercept) |  0.95701699 |  1.12747445 |\n",
       "| TIMEPTP10 | -0.18618492 | -0.04638226 |\n",
       "| TIMEPTP30 | -0.20118259 | -0.06278061 |\n",
       "| GROUPaV1-gV5 | -0.17302595 |  0.04272109 |\n",
       "| GROUPgV1-aV5 | -0.16425876 |  0.04876608 |\n",
       "| V1pV5a | -0.03325171 |  0.03619419 |\n",
       "| GROUPaV1-gV5:V1pV5a | -0.03657595 |  0.04489294 |\n",
       "| GROUPgV1-aV5:V1pV5a | -0.05003009 |  0.02373085 |\n",
       "\n"
      ],
      "text/plain": [
       "                    2.5 %       97.5 %     \n",
       ".sig01               0.04206471  0.13296624\n",
       ".sigma               0.12777705  0.17790788\n",
       "(Intercept)          0.95701699  1.12747445\n",
       "TIMEPTP10           -0.18618492 -0.04638226\n",
       "TIMEPTP30           -0.20118259 -0.06278061\n",
       "GROUPaV1-gV5        -0.17302595  0.04272109\n",
       "GROUPgV1-aV5        -0.16425876  0.04876608\n",
       "V1pV5a              -0.03325171  0.03619419\n",
       "GROUPaV1-gV5:V1pV5a -0.03657595  0.04489294\n",
       "GROUPgV1-aV5:V1pV5a -0.05003009  0.02373085"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>NumDF</th><th scope=col>DenDF</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>TIMEP</th><td>0.39976477</td><td>0.19988239</td><td>2</td><td>72.01900</td><td>8.3788468</td><td>0.0005351423</td></tr>\n",
       "\t<tr><th scope=row>GROUP</th><td>0.03786626</td><td>0.01893313</td><td>2</td><td>52.40166</td><td>0.7936558</td><td>0.4575483541</td></tr>\n",
       "\t<tr><th scope=row>V1pV5a</th><td>0.03018950</td><td>0.03018950</td><td>1</td><td>87.71862</td><td>1.2655104</td><td>0.2636793982</td></tr>\n",
       "\t<tr><th scope=row>GROUP:V1pV5a</th><td>0.04806315</td><td>0.02403158</td><td>2</td><td>94.42652</td><td>1.0073769</td><td>0.3690658192</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Sum Sq & Mean Sq & NumDF & DenDF & F value & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tTIMEP & 0.39976477 & 0.19988239 & 2 & 72.01900 & 8.3788468 & 0.0005351423\\\\\n",
       "\tGROUP & 0.03786626 & 0.01893313 & 2 & 52.40166 & 0.7936558 & 0.4575483541\\\\\n",
       "\tV1pV5a & 0.03018950 & 0.03018950 & 1 & 87.71862 & 1.2655104 & 0.2636793982\\\\\n",
       "\tGROUP:V1pV5a & 0.04806315 & 0.02403158 & 2 & 94.42652 & 1.0073769 & 0.3690658192\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 6\n",
       "\n",
       "| <!--/--> | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | NumDF &lt;int&gt; | DenDF &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| TIMEP | 0.39976477 | 0.19988239 | 2 | 72.01900 | 8.3788468 | 0.0005351423 |\n",
       "| GROUP | 0.03786626 | 0.01893313 | 2 | 52.40166 | 0.7936558 | 0.4575483541 |\n",
       "| V1pV5a | 0.03018950 | 0.03018950 | 1 | 87.71862 | 1.2655104 | 0.2636793982 |\n",
       "| GROUP:V1pV5a | 0.04806315 | 0.02403158 | 2 | 94.42652 | 1.0073769 | 0.3690658192 |\n",
       "\n"
      ],
      "text/plain": [
       "             Sum Sq     Mean Sq    NumDF DenDF    F value   Pr(>F)      \n",
       "TIMEP        0.39976477 0.19988239 2     72.01900 8.3788468 0.0005351423\n",
       "GROUP        0.03786626 0.01893313 2     52.40166 0.7936558 0.4575483541\n",
       "V1pV5a       0.03018950 0.03018950 1     87.71862 1.2655104 0.2636793982\n",
       "GROUP:V1pV5a 0.04806315 0.02403158 2     94.42652 1.0073769 0.3690658192"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# update.packages(ask=FALSE)\n",
    "# install.packages(\"broom\")\n",
    "library(simr)\n",
    "library(Matrix)\n",
    "library(lme4)\n",
    "library(emmeans)\n",
    "library(lattice)## LOADING AND INSPECTING THE DATA\n",
    "library(lmerTest) ## INFERENTIAL TESTS\n",
    "library(mice)\n",
    "library(ggstatsplot)\n",
    "library(rstantools)\n",
    "library(ggpubr)\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "# ndr[45:88,]\n",
    "dim(ndr)\n",
    "\n",
    "## TURN NUMERICAL VALUES INTO FACTOR/CATEGORICAL VARIABLES\n",
    "ndr$TIMEP <- factor(ndr$TIMEP)\n",
    "ndr$GROUP <- factor(ndr$GROUP)\n",
    "ndr$SUBJECT <- factor(ndr$SUBJECT)\n",
    "str(ndr)\n",
    "levels(ndr$GROUP)\n",
    "\n",
    "## SIMPLE PLOTS\n",
    "# plot(NDR~TIMEP,data=ndr,col=\"grey50\",pch=\"o\")\n",
    "# xyplot(NDR~TIMEP,groups=GROUP,data=ndr,pch=\"+\",cex=1.5)\n",
    "# options(repr.plot.width = 8, repr.plot.height = 6)\n",
    "# ggline(ndr, x = \"TIMEP\", y = \"NDR\", add = \"mean_sd\", color = \"GROUP\", palette = \"jco\", size=2, point.size=2,\n",
    "#       legend=\"top\", legend.title=\"GROUP\", font.legend=c(24, \"bold\"))+ ylim(0.6, 1.2) +\n",
    "# theme(axis.title.x=element_text(size=24, face=\"bold\"), axis.title.y=element_text(size=24, face=\"bold\"), \n",
    "#       axis.line=element_line(size=2), axis.text=element_text(size=24, face=\"bold\"))+\n",
    "# stat_compare_means(aes(group= GROUP), size=7, label = \"p.signif\")\n",
    "\n",
    "\n",
    "## IDENTIFY OUTLIERS FOR EACH GROUP OR ACROSS TIMEP\n",
    "# ndr_filt <- filter(ndr, TIMEP==c('TP0') | TIMEP==c('TP10') | TIMEP==c('TP30'))\n",
    "# ndr_filt <- filter(ndr, GROUP==c('Sham','aV1-gV5','gV1-aV5'))\n",
    "# dim(ndr_filt)\n",
    "\n",
    "# options(repr.plot.width = 14, repr.plot.height = 21)\n",
    "# betweenstats because it was a parallel design n=45\n",
    "# grouped_ggbetweenstats(data=ndr, x=TIMEP, y=NDR, grouping.var=GROUP, type = \"np\", pairwise.comparisons=FALSE,\n",
    "#                       outlier.tagging=TRUE, outlier.label=X, outlier.color='red', effsize.type=\"eta\", outlier.coef=1,\n",
    "#                        # arguments relevant for ggstatsplot::combine_plots\n",
    "#                       annotation.args = list(title = \"NDR over TIMEP and GROUPs\"),\n",
    "#                       plotgrid.args = list(ncol = 1))\n",
    "# ## Tukey=1.5\n",
    "# ndr$NDR[61] <- NA\n",
    "# ndr$NDR[68] <- NA\n",
    "# ndr$NDR[101] <- NA\n",
    "# # Tukey=1.2\n",
    "# ndr$NDR[48] <- NA\n",
    "# ndr$NDR[78] <- NA\n",
    "# ndr$NDR[88] <- NA\n",
    "# ndr$NDR[56] <- NA\n",
    "# # Tukey=1\n",
    "# ndr$NDR[113] <- NA\n",
    "# ndr$NDR[45] <- NA\n",
    "# ndr$NDR[56] <- NA\n",
    "# ndr$NDR[90] <- NA\n",
    "# ndr$NDR[124] <- NA\n",
    "# ndr$NDR[131] <- NA\n",
    "# ggline(ndr, x=\"TIMEP\", y=\"NDR\", add=\"mean_sd\", color=\"GROUP\", palette=\"jco\", size=2, point.size=2,\n",
    "#        legend=\"top\", legend.title=\"GROUP\", font.legend=c(24, \"bold\"))+ ylim(0.6, 1.2) +\n",
    "# theme(axis.title.x=element_text(size=24, face=\"bold\"), axis.title.y=element_text(size=24, face=\"bold\"), \n",
    "#       axis.line=element_line(size=2), axis.text=element_text(size=24, face=\"bold\"))+\n",
    "# stat_compare_means(aes(group =GROUP), size=7, label = \"p.signif\") \n",
    "\n",
    "# RANDOM INTERCEPT MODEL\n",
    "# ndr$TIMEP <- relevel(ndr$TIMEP,\"TP0\")   # changed the intercept to TIMEP:TP0\n",
    "# mlm1 <- lmer(NDR ~ 1 + TIMEP*GROUP + (1|SUBJECT), data=ndr, REML=TRUE)#, na.action=\"na.fail\")\n",
    "# summary(mlm1)\n",
    "# anova(mlm1)\n",
    "# # difflsmeans(mlm1, test.effs=\"TIMEP+GROUP\", ddf=\"Kenward-Roger\")\n",
    "# # write.csv(difflsmeans(rint, test.effs=\"GROUP*COHA\"),\"Interaction.csv\")\n",
    "# emm = emmeans(mlm1, ~ TIMEP+GROUP, ddf=\"Kenward-Roger\")\n",
    "# pairs(emm, simple='each', adjust=\"none\")\n",
    "# confint(pairs(emm, simple='each', adjust=\"none\"))\n",
    "\n",
    "# No Need to change the intercept to TIMEP:TP10/TP30 \n",
    "# mlm2 <- lmer(NDR ~ 1 + TIMEP+GROUP*V1pV5a + (1|SUBJECT), data=ndr, REML=TRUE)#, na.action=\"na.fail\")\n",
    "# summary(mlm2)\n",
    "# confint(mlm2)\n",
    "# anova(mlm2, type=2)\n",
    "# plot(mlm2, id=0.05) ## Residuals plotted as white noise mean that they have dist. close to N, mean 0 and constant variance\n",
    "ndr$GROUP <- relevel(ndr$GROUP,\"Sham\")   # changed the intercept to GROUP:SHAM\n",
    "mlm3 <- lmer(NDR ~ 1 + TIMEP+GROUP*V1pV5a + (1|SUBJECT), data=ndr, REML=TRUE)#, na.action=\"na.fail\")\n",
    "summary(mlm3)\n",
    "confint(mlm3)\n",
    "anova(mlm3, type=2)\n",
    "\n",
    "## COMPARING RANDOM EFFECTS BY INFORMATION CRITERIA\n",
    "# AIC(rint) ; BIC(rint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Scale for 'y' is already present. Adding another scale for 'y', which will\n",
      "replace the existing scale.\n",
      "\n",
      "Warning message:\n",
      "“Removed 13 rows containing missing values (geom_point).”\n",
      "Warning message:\n",
      "“Removed 24 row(s) containing missing values (geom_path).”\n",
      "Warning message:\n",
      "“Removed 13 rows containing missing values (geom_point).”\n",
      "Warning message:\n",
      "“Removed 24 row(s) containing missing values (geom_path).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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ADQMI3B7oUXXrjvvvt+/OMfe0/f+973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Tno582jF0LTPMEWANJAsENSyHPQVXikC80h2wFAqrh4\nAolwPYSGuPQ1VdFpDwCQGMEOcZHnDJPjmS9BgCPbAUBKOBQLGKdxXlP0JRQmTHUDP94a/rJo\n43PZqgQAkBKCHWAoE8a4CBGpLjQnp+Jd9EghJ/wBsAQOxQL4i+hUl4NiHv998+gFjgsDMD+C\nHYCkZCXzMU4GACkh2AHIMtIbAGiFYAcg+6Kz3brayqwEPo63ArA0Lp4AYAomGbdbV1tJtgNg\nXYzYAUhKTl0VCwAWRbAD8BekNwCwNA7FAvgf1GwXfg1srqW9eEdjTXKwGAASINgBiCHXwlwE\nNcOF4h2RDoBVEOwAIDbyHADL4Rw7AAAASRDsAAAAJEGwAwAAkATBDgAAQBIEOwAAAEkQ7AAA\nACRBsAMAAJAEwQ4AAEASBDsAAABJEOwAAAAkQbADAACQBMEOAABAEo5sFwAAVvKrT3dHzGmc\n15SVSgAgGsEOgOQGfrw1/GXRxufSXlV0qlNnku0AmASHYgHILCLVxZyTuZiBDwCMR7ADIK14\nGS69bEd6A2B+BDsAAABJEOwAAAAkQbADICc9zqUDAJMj2AGwpDePXnjz6IUEC2Ry9WtMCS59\n5apYACbB7U40EAwG/X7/2NhYJivx+/1CCJ/PpyiKRnXpzu/3K4qS4Q9upEAgoP7fQjUHg8Fg\nMGihgtUOrGvNv/ygKzT9s8PnhRDfWjI75pLqNx5TRHlJ9uT/ffs39l3YO+HaDKAoirV++4QQ\niqKMj4/bbLZsF5KsYDAohMi8Zgvt1SEBgp0GFEUJBoM+ny+Tlah7kEAgYKFdgPqvZoY/uJFC\nG9lCNWvSu4ynKIpONf/f4xejZ/7iWOfkW/4QMfMbX/qm86knvf/6WvTy7u9siCgv+YIfu+1/\nNf/x7fBWRDZ+C9QdhbU6hrqRLRfsMq9ZTeEaFQVMgGCngby8PJfLNWXKlExWMjo66vP53G63\ny+XSqjC9eb1eRVEmTZqU7UKS5fP5xsfHXS5XQUFBtmtJlt/vHx0dzbB3GUlRFK/Xm5eXp0fN\nbx69EPMX5PzYuwtdN0XMPPD5/2uc1zTlu/8nmRsU+3y+5Atec8+3klxSP+rovoU6hhCir69v\n8uTJdrtlTgEaHBwMBAKZ12y32y0UZ2F1BDsA1nZ+7F0hxEddXyycHZntVJqfbAcApmWZv5wA\nIFXcUhhAriHYAQAASIJgB0AG8Y7DAkBOIdgBsIx1tZXZLgEATI1gB8BKYma7eMN13DcYQK7h\nqlgAFhOV7b4T8yIJUh2AHMSIHQDLa5zXFBHjSHUAchMjdgAkQZgDAEbsAAAAJMGIHQAkJfxM\nPkYHAZgTI3YAMLGI6zN+9eluHmsBwIQIdgAwgXgZjmwHwGwIdgAAAJIg2AFAIgzLAbAQgh0A\nAIAkCHYAAACSINgBQCLc2QSAhRDsAGAC8bIdmQ+A2RDsAGBi0RmOVAfAhHjyBAAkhSQHwPwY\nsQMAAJAEwQ4AAEASBDsAAABJEOwAAAAkQbADAACQBMEOAABAEtzuBDCvX326OxgM+v1+l8vF\nvTYAABMi2AEm9atPd0e/lC/eDfx4a8Scoo3PZaUSAJAAwQ4wo4hUJ6voVKfONCbbhW9kr9fr\n7nHLl5sB5BrOsQNMJ0GqkynwxUx1E76llZhbUqbNCyA3EewA4C/IdgAsjWAHIOeQ3gDIimAH\nAAAgCYIdAACAJAh2gOkkuDZTpss2E1z6yh1PACA9BDvAjGIGOJlSnSpmgDMg1eVIdAaQg7iP\nHWBSasLw+/2jo6OFhYXZLkcvaoxT729i5EBd47wmLqEAIB+CHYDsy8qx14hsl9JYXfid9jhw\nDMA8CHYAclcozHk8niQ/En3zZOOHGwEgHs6xAwAAkATBDgCSld3HoAHAhAh2AAAAkiDYAQAA\nSIJgBwAAIAmCHQAAgCQIdgCQLB6DBsDkCHYAkIJsPQYNAJLBDYoBIDXEOACmxYgdAACAJAh2\nAAAAkiDYAQAASIJgBwAAIAmCHQAAgCRMfVXstWvXRkdHw+dMnz59ypQp2rbS39/f19enaxMA\nAAAGMGmwUxRFCLF9+/YTJ06Ez3/22Wfr6uqEEDabTatWDh48+NZbb+nUBAAAgGHMGOwuXbq0\nZcsWIcT169cj3tq9e/f+/fvnzZv39NNPZ9iK3+9/6aWXrl27Fj5cp20TAAAARjJdsDt79mxz\nc3N3d3fMd3t7e3t7ewcGBux2+5o1ayZNmpReKz09PTt27Dh37tzIyIhOTQAAABjMdMGup6fn\n9OnToZfz58+/66671OnDhw97PB4hhMfjOXny5OrVq9Nroqur6/e///3x48ejmxBCnDp1qqur\nK8MmAAAAjGeuYHfx4sXPPvss9PKOO+54+OGHlyxZor70+XzHjx9Xj8/6fL62traFCxcWFRWl\n2sqFCxd+97vfxWxCCDFt2rRDhw51d3dn0gQAAIDxzHW7k8OHD7/zzjtCCJvNVlJS0tTUFB65\n1q5du3jx4sLCQiHE0NDQ1q1b4x2xTWBoaGhgYCBeE0KIRx55ZPny5Zk0AQAAkBXmGrELcTqd\nmzZtmj17dsT81atXFxYW7ty5M+01/+Y3vzlw4ECCJgAAACzKpMFOCOF2u+32yAFFp9PpdDoz\nWa3f7x8fH0/QhBCipqZm7ty56nRFRUUmzQEAABjGRMHuwIEDZ86cEUKUlpauXLly2rRpMRer\nrq5uaGhQR932798vhFiwYIG2lRQXFxcXF2u7TgAAAL2Z6Bw79XJUIURRUdHy5csLCgpiLnbb\nbbfdd999oY+kdw7c1KlTH3roocmTJ6dbLAAAgOmYaMTOAF1dXb29vUKIGTNmfPvb31ZnXrt2\n7dq1a6FlZs2aFW+wEAAAwMxyK9ht3769vb099HJkZCQYDL777ru//vWvQzPXr19fU1OTl5fH\nrYkBAIC15FawC+fz+f75n//56tWro6Oj4fN37dq1b9++u++++x//8R8TfLylpSUYDKrTV65c\ncbvdY2NjmdTj9/vVqtQn2FqC3+9XFCXDH9xIgUBA/b+1arZWwWoHDgaD0TX/8oOu8JffWjLb\nqKImZq2eLIRQFMVyNQeDwfHxcQs9hlvdyWdes4X26pBAjga7y5cvb968+Y9//KPX6414a2ho\nSAhx5syZV1555amnnop3qt/3vvc9NYoJIaqrq6urqwcHBzMvLCJlWoK1/mkRQoyNjVmuZk16\nl5H8fn9Ezbv/cDlimZ8dPt/05VsNLGoCltvIwoI1qztYa8m85kAgQLaDYXI02I2MjKgPLqur\nq4u4ld0HH3zw3//93wMDA62trYWFhY8++ujNN98cvYannnoq9It69epVp9OZ4aUYPp9vfHzc\n7Xbn5eVlsh4jqSN2Gd6AxkiBQMDr9bpcLgvVHAwGfT5ffn5+tgtJwfDwcF5entvtDs3Z8WG3\ny+WKXvLt071rFt9mYGlxjY6OWuvsi9HRUUVR4v3laU6jo6Nut9tCI3ZjY2N+v7+goCDDmmPe\nVwvQSY4GOyGE3W6///77//Zv/7aysjJ8fkFBgaIoFy5c8Hq9v/vd7xYtWhQz2P3d3/1daPrt\nt98eHBzM/F+F8fFxl8sV898/c/J6vYqiWOifQ5/P5/V6HQ6HhWr2+/3BYNBCBSuKoga78Jod\njri7GpP8aF6v1ySVJEk92mCtmsfGxuLdPdSc/H6/3+/PvGa73W5bJiwmAAAcbElEQVShOAur\ns8wvmOYcDseaNWsiUp0Qor6+vqGh4dZb/3yE6PLly/39/YZXB8jjzaMXsl0CAOSKHA12Npst\nwV9gS5cuXb9+vTr905/+9IMPPjCqLgAAgPTlaLCrqKj4yU9+MnPmzGwXAshvXW3kuDgAQCc5\neo6d0+ksKyvLdhUAAABaMtGIXW1t7dy5c4UQHo+nubk53mX8HR0dx44dU6fr6uqqqqrSaAKA\nkeIN2jGYBwDaMlGwq6uru/POO4UQN27c2LNnT7xg98knn7S0tKjTy5YtSynYhZoYHh5ubW2N\nvokdAJ1EZzhSHQBozmKHYvv7+wcGBjJfz5UrV7Zs2bJt27bQ1a/hRkZGvvjiC3V6+vTp1rpT\nFGBaJDkA0JvFgt2uXbuOHDmidystLS07duxQpzds2FBdXa13iwAAAJkzV7BraGjIz8/fu3ev\nz+d7+eWXXS5XfX19fX29+u6rr77a1tamPsirsLDw+eefj74LnRCitbV137596vQTTzyxYMGC\nBE2sW7cuYoG9e/ceOnRofHxcfelyuSz0KAgAAJDLzBXsSkpK1FuQKIrS1dUlhAgEAh0dHeq7\nbW1toXsFOxyOOXPmxLzr+sDAQOgj0c/4i2hi37597733XvgC586du379uhCioKCgqalp1qxZ\n2v18AAAAOjJXsBNCVFRU1NTUvP/+++rLzs7Ozs7OiGVKS0vr6urSftxneBPt7e0xl1GbWLFi\nRfjzLgEAAMzMdMGuqqpq1apVfX19Qoju7u6Ix3mVl5cXFxdXVlY2NjaauQkAAADjmS7YCSHK\nyso2b94shNi2bdupU6fC31q5cuWSJUsSf9zlck2dOlWdjjeql2ETAAAAJmTGYBfyzDPPpPGp\nmpqampoaXZsAAAAwIRPdoBgAAACZINgBAABIgmAHAAAgCYIdAACAJAh2AAAAkiDYAQAASMLU\ntzsBAEzoV5/ujpjTOK8pK5UAyDpG7ADAwqJTXbyZAHIBwQ4AJES2A3ITwQ4ArIr0BiACwQ4A\nAEASBDsAAABJEOwAwKq4+hVABIIdAEiIzAfkJu5jByBHDfx4a2ja5/UOuN1FG5/LYj3paZzX\nxH3sAIQwYgcgF4WnusQzza9xXlMoyYVPA8hBjNgByDkWDXCJkecACEbsACCclJkPQO5gxA5A\nNr159EL4y3W1ldmqBAAkwIgdgKyJSHUx5wAAkkewA5Ad8TIc2Q4A0kawA4C/sOIdTwAghGAH\nwHT0HrSLl95IdQCsjmAHIBcVbXwuIsaR6gBIgKtiAZiOYdfGhsJcwOMxpkUA0BUjdgAAAJIg\n2AHIjnjDctzKDgDSRrADkDXRGY5UBwCZ4Bw7ANlEkgMADTFiBwAAIAmCHQAAgCQIdgAAAJIg\n2AEAAEiCYAcAACAJgh0AAIAkCHYAAACSINgBAABIgmAHAAAgCYIdAACAJAh2AAAAkiDYAQAA\nSIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJgh0AAIAkCHYAAACSINgBAABIgmAH\nAAAgCYIdAACAJAh2AAAAkiDYAQAASMKR7QJkEAwGfT7f6OhoJivx+XxCiPHx8UAgoFFduvP7\n/YqiZLuKFKjb1u/3Z/hlGSkYDAYCAQsVrLJczYqiWK5gy9UcDAa9Xq/NZst2IclS9xiZ1xwM\nBq21q4SlEey0YbPZMvzNVz+e+XoMZq2CQ6VarmYLFaz+A2atjqGyXMHCgjVbtGNosnsHjEGw\n04Ddbnc4HG63O5OVKIoyNjbmdDpdLpdWhRlAUZQMf3AjqQOrmX9ZRvL7/YFAwEIFK4oyPDxs\nt9stVLMQYnR01HIFCyGsVbPX683Pz7fbLXMKkM/n8/v9mddsxTgL67LMLxgAAAASI9gBAABI\ngmAHAAAgCYIdAACAJAh2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEAAEiCYAcA\nACAJgh0AAIAkCHYAAACSINgBAABIgmAHAAAgCYIdAACAJAh2AAAAkiDYAQAASIJgBwAAIAmC\nHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJgh0AAIAkCHYAAACSINgBAABIgmAHAAAgCYIdAACA\nJAh2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJgh0AAIAkCHYA\nAACSINgBAABIgmAHAAAgCYIdAACAJAh2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg\n2AEAAEiCYAcAACAJgh0AAIAkCHYAAACScGS7AACy8b/xMyUvbyA/XwhRtPG5bJcDADmEYAdA\nMwM/3hpzDvEOAIzBoVgAAABJEOwAaCN6uC6ZtwAAGiLYAQAASMLU59hdu3ZtdHQ0fM706dOn\nTJmia6O9vb3Dw8Nut3vmzJm6NgQAAKAtkwY7RVGEENu3bz9x4kT4/Geffbaurk4IYbPZdGp3\n165dLS0t99577w9/+EM9mgAAANCJGYPdpUuXtmzZIoS4fv16xFu7d+/ev3//vHnznn76aT2a\nfuWVV06fPq3HmgHpFW18Lt65dFwVCwDGMF2wO3v2bHNzc3d3d8x3e3t7e3t7BwYG7Hb7mjVr\nJk2apFW7Ho/nl7/85ZkzZ4aGhrRaJwAAgJFMF+x6enrCx8zmz59/1113qdOHDx/2eDxCCI/H\nc/LkydWrV2vY7ujo6Icffuj3+zVcJ5BrijY+pyjKyOYfhc/JYj0AkGvMFewuXrz42WefhV7e\ncccdDz/88JIlS9SXPp/v+PHj6vFZn8/X1ta2cOHCoqKizNv1eDzt7e3qiX0AMuR4cr3L5dLk\ndxMAkBJz3e7k8OHD77zzjhDCZrOVlJQ0NTWFUp0QYu3atYsXLy4sLBRCDA0Nbd26Nd4R25SM\njIycPHnyjTfeCAQCma8NAAAgW8w1YhfidDo3bdo0e/bsiPmrV68uLCzcuXOnhm0dPHhwz549\nGq4QAAAgK8w1YhfO7Xbb7ZHlOZ1Op9OpYSs7d+48ePDg+Pj4jBkzXnrppfLycg1XDgAAYCQT\nBbsDBw6cOXNGCFFaWrp+/fpp06bFXKy6urqhoUGd3r9//9mzZzNp9E9/+lNvb68QwuVyzZs3\nLz8/P5O1AQAAZJGJgt2pU6e6urqEEEVFRcuXLy8oKIi52G233XbfffeFPpL2aXbBYPDYsWM9\nPT1CiFtuuWXp0qU63fQYAADAGCY9x05vXq/3008/3blzZ29vb2lp6dKlSx9//PFsFwUAAJCR\nHA12n3/++YsvvqhOL1u2bNWqVdmtBwAAIHM5Guwyt3PnztB9765evTpt2rTR0dFMVujz+YQQ\n4+PjFrrrit/vt9bN/9Rt6/f7M/yyjBQMBgOBgIUKVlmuZkVRLFew5WoOBoNer9dCJ72oe4zM\naw4Gg9baVcLScjHYnT59+q233lKnH3/88dra2jRW8vrrr4ceU1FdXV1dXT08PJx5bV6vN/OV\nGGx8fDzbJaRmfHzccjVb7pkogUBAk98II1muYGHBmkdGRrJdQsoyrzkYDGpSCZCMnAt2ra2t\nBw8e/PTTT/Py8r7+9a/X1tbefPPNaaxn27Ztoem2tjaHwzF16tRMChsbG/N6vZMnT3Y4LPOl\njI+PK4pioUuJ/X7/8PCw2+22UM2BQGBsbCzetUQmpCjKwMCA0+m0UM1CiKGhoSlTpmS7ihQM\nDg4KIdQbtlvF0NDQ5MmTLTRiNzIy4vP5ioqKMqw5Ly/PQj81rM4yGUIrH3/88UcffSSEyMvL\nW7Fixa233preeu6///7QdHd39+DgYIY32FOHZPLy8rS9UZ+uAoGAoigWKlhlt9stVLPNZvP5\nfBYqWD3kZLPZLFSzyloF22w2y/322Ww2h8MRfYNS01JLzbxmUh2MlFvB7sqVK319fUIIt9s9\ne/Zsa+0TAQAAEsuhYBcMBl9//fX29nabzVZRUbFly5ZsVwQAAKClHAp2L7zwQmdnpxDiK1/5\nytq1a7NdDgAAgMZyKNhdvnxZvea0s7Nzx44dMZdRH0QhhOjq6goN6S1fvnzhwoWG1AgAAJA+\nEwW72tpar9d7/vx5j8fT3Nz84IMPxrzgq6Oj49ixY+p0XV1dVVVVqg319PSEAlw8Ho/nww8/\nVKfvuusugh0AADA/E12dVFdXd+eddwohbty4sWfPHvVi/miffPJJS0uLOr1s2bI0gh0AAICU\nTDRil4z+/v6BgYH0Pjtz5ky32514mRs3bqi3rs3Pz7/pppvUmda6HRcAAMhZFgt2u3btOnLk\nSHqf3bx584TL/NM//ZN6gcW8efO+//3vqzPz8vLSaxEAAMBI5gp2DQ0N+fn5e/fu9fl8L7/8\nssvlqq+vr6+vV9999dVX29ra1Bv5FhYWPv/885WVldEraW1t3bdvnzr9xBNPLFiwQJ12uVwT\nFhC6jaTdbk9meQAAAPMwV7ArKSmZOXOmEEJRlK6uLiFEIBDo6OhQ321ra+vv71enHQ7HnDlz\nJk2aFL2SgYGB0EeGhoYMKBsAAMAMzBXshBAVFRU1NTXvv/+++rKzs1M9NhqutLS0rq6O50YA\nAACEM12wq6qqWrVqlfrgr+7u7tAQnaq8vLy4uLiysrKxsTFLBQIAAJiU6YKdEKKsrEy90GHb\ntm2nTp0Kf2vlypVLlixJ/HGXyzV16lR1OtVRvcLCQvWzkydPTumDAAAAWWfGYBfyzDPPpPGp\nmpqampqa9Fr84Q9/mN4HAQAAss5ENygGAABAJgh2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQI\ndgAAAJIg2AEAAEiCYAcAACAJgh0AAIAkCHYAAACSINgBAABIgmAHAAAgCYIdAACAJAh2AAAA\nknBkuwBJNDc3Hz16NJM1BIPBYDCYl5dns9m0qkpvwWBQCGG3W+bPA0VRAoGA3W63Vs1qx8h2\nISnw+/02m81aNQcCAcsVrCiKw2GlfXjObuTu7m5N6gGSYVMUJds1WN74+LjX681wJb/+9a93\n7tz53e9+94EHHtCkKgOoncdCSbS9vf3FF1/85je/uXr16mzXkgJFUSy0kYeHhxsbG++9994f\n/OAH2a4lBdbayEKIv//7vx8ZGfn3f//3bBeSAstt5C1bthw/fvwXv/jFjBkzMlxVYWGhtX52\nWJeV/tozLZfL5XK5MlyJ3W4fHBx0Op1FRUWaVIVo+fn5g4ODNpuNjawfm802ODjo9/vZyLry\ner3Dw8NsZF0Fg8HBwcGCggK2MyzEMgekAAAAkBjBDgAAQBIcijWL2bNnL1++vLS0NNuFyOym\nm25avnz5nDlzsl2IzBwOx/Lly6uqqrJdiOQWLVo0Ojqa7Sokd/fddweDQbfbne1CgBRw8QQA\nAIAkOBQLAAAgCYIdAACAJAh2AAAAkuDiCV0MDQ3duHEjyYVnzpyZ4cm5165diziNevr06VOm\nTMlknZaj00Yw+Ks0DwM6Ff1W0G91w04YOYtgp4uTJ09u27YtyYV/9KMfLViwIL2G1Gtftm/f\nfuLEifD5zz77bF1dnbDUYyHSputGMOyrNA8DOhX9VtBvdcZOGDmLYGdhly5d2rJlixDi+vXr\nEW/t3r17//798+bNe/rpp7NRmnHYCNoyYHvylQk2giz4HmFCBDurOnv2bHNzc7xnS/f29vb2\n9g4MDNjt9jVr1kyaNMng8ozBRtCWAduTr0ywEWTB9whzItjpbtGiRWVlZQkWSO/x0j09PadP\nnw69nD9//l133aVOHz582OPxCCE8Hs/Jkyet9cD75LW3t7/77ruhjRC9nU+dOtXV1eXxeI4d\nO1ZUVLRixYoM7/+s01dpHgZ0Kvot/dZ47ISRUwh2uvvqV7/6la98Rdt1Xrx48bPPPgu9vOOO\nOx5++OElS5aoL30+3/Hjx9VDAz6fr62tbeHChfI9xLqtre2//uu/hBB2u33BggWPPfbY3Llz\nwxeYNm3aoUOHuru7R0dH9+7de88992T4D6QeX6V5GNCp6LeCfpsN7ISRU7jdiSUdPnz4nXfe\nEULYbLaSkpKmpqbQDkUIsXbt2sWLFxcWFgohhoaGtm7dGu9ggXX19fWNjIyo0w6H48knn4z4\n11EI8cgjjzQ0NBQXF6svPR4Pj2BKwIBORb+l30qDzgzTIthZm9Pp3LRpU3V1dcT81atXP/bY\nY1kpyRivvfZaS0vLhIvV1dWFzlzetm3bsWPH9C1LCgZ0KvptYvRbC8nZzgzT4lCs9v7jP/5D\n/UvO6XT+wz/8w913361rc263226PDOhOp9PpdOrabnaNjY35/X4hRHl5+bPPPltSUhJzsby8\nPJfLpU6Pj48HAoGUWjH4qzQPAzoV/ZZ+qx92wshljNhp79q1a1euXBFC2Gy2OXPmqKPxGjpw\n4MCZM2eEEKWlpevXr582bVrMxaqrqxsaGtTp/fv3nz17VtsyTCI/P7+qqir0r6C29P4qzcOA\nTkW/DUe/1RU7YeQyRux019bWdvXq1fA5f/VXfzVr1qy0V6heNCeEKCoqWr58ebzFbrvttvvu\nu+/AgQPqR+69916Z7kH6wAMPqNvQyAv6NP8qzcOATkW/FfTbLGEnjJxCsNNRMBjs6Oj4/e9/\nf+7cufD53/jGNxYuXDhlypTZs2dnqTTL+5u/+ZtkFuvt7Q1dufalL31p+vTp6TXHVwlN0G8N\nxhZADiLY6cjv92/dujV6fnNzc3Nz84IFC773ve8VFBTwwBmdeL3elpaWXbt2qS+//e1vp/3n\nMl8lDEO/1RBbADmIc+yy5vz58y+88MLw8HC2C5HWrl27fvOb3xjQEF8lNES/NQxbAFJixE53\njz/++J133hl6+eabb/7pT38SQoyPj1+6dOlf/uVf1q5de/vtt2evQDn9/Oc/P3HihHrPsMLC\nwieffDLzYy58ldAb/VYPbAHkFIKdjvLy8r7+9a/X1tbeeuutoZmPP/54X1/fxx9/3Nra6vP5\n2tvbh4aGslikfAYGBn77298eP35cfaRPWVlZQ0PD/fffn8kViHyV0Bv9Vg9sAeQggp32Kisr\n6+rqhBB5eXmPPvpoxJXwS5cuFULYbLbW1lZ1zunTp4uLi3PqIjWddHV1ffbZZx6PZ//+/eqt\nv8rLy5ctW/bQQw+lt0K+ShiAfqs5tgByGcEuWVeuXIn3YB+n01leXh56WVNTU1NTk3htU6dO\nvfXWWy9fviyEaG5uvummm9inqJLfzhF6enoOHjz4n//5n6E5paWl9fX1jz76aNrF8FVCb/Rb\nPbAFkMsIdsl6/fXX29vbY75VVlb2xhtvpLS2pUuXTps27cUXX9SiNKmksZ2DwaAQ4t/+7d9O\nnDghhLDZbOpd4BsbG9W/2nXFV4n00G+ziy0AWRHsYG0XL158+eWXhRA3btxQ58yYMeP73/++\nw+EIPUYdMBv6LQCdEOyStXLlyq997Wsx35o0aZLBxUgspe189uzZt99++/PPP1df/vVf//Xi\nxYsnTZpUUVHBjalgWvRbAPoh2CVr/vz5ySx27Nixnp4eIURxcXF9fb0eldTW1nq93vPnz3s8\nnubm5gcffDDmkxA7OjqOHTumTtfV1VVVVelRjOaS3M5CiDNnzhw8eFB9YqMQYvHixQ899JCG\nT+wx4Ks0DwM6ldz9Nnn0W72xE0aOI9hp7MiRI+opYpWVlQn2KVevXv3kk0/Sa6Kurq6rq+v8\n+fM3btzYs2fPokWLYu5TPvnkk5aWFnV62bJl8u1TPvroo5MnTwoh7Hb7ggULHn300blz52q4\nfgO+SvMwoFPRb1X0W72xE0aO48kTevH5fFevXlVvXhDtD3/4w1tvvaVOT58+vaCgQNvW+/v7\nBwYGtF2nqXzxxRfqradcLtesWbO+853vaPuvY7jsfpXmYUCnot9qiH7LThi5iWCnl0uXLm3c\nuPHatWsTLrlhw4avfvWr2ra+a9eu3/72t9qu01R++tOfHj16VAhRXl6+devWGTNm6NdWdr9K\n8zCgU9FvNUS/ZSeM3JT3gx/8INs1SGXu3LlDQ0Pd3d2Kovh8vrNnz86aNWvmzJmhBV599dXm\n5ub29nb1qUFCiPr6+ptvvjliPa2trT/5yU8OHTp06NChW265JXwNQojy8nK3233u3LlgMPjx\nxx8fOXJECDFnzpxQE6dOnVLvBldYWLhp06aqqiqn06nfT228w4cPX7lyRQgxffr0hx9+OO1T\nzhNsZ62+SqvQpFPRbxOj3xqAnTByHOfYaaysrCx0twJFUbq6uvbt2/fee++FFmhra+vv71en\nCwoKmpqaYt4Vc2BgoKOjQ52OftxNSUmJupdRmxBCBAKB0PLhTTgcjjlz5kh83e7169dfe+21\nJBeuqam55557wuck2M5afZVWoUmnot8miX6rH3bCyHEEO+3Nnz+/q6srdNVbvNvtlpaW1tXV\nrVixwu12p9FKRUVFTU3N+++/r77s7Ozs7OyM2YTcfyb29/cfOnQoyYVnz54d8Q9kYsZ8leZh\nQKei36rot7piJ4xcRrDT3pe//GWn0xkMBhVF6ejoGBsbC3/3jjvuUP90q6ysbGxsTLuVqqqq\nVatW9fX1CSG6u7tDfx2qysvLi4uLM2wCxnyV5mFAp6LfGiDX+m00dsLIZQQ7XSxcuHDhwoU+\nn++FF15QT6kJ2bBhw+233z7hGlwu19SpU9XpeH/tlZWVbd68WQixbdu2U6dOhb+1cuXKJUuW\npFm9FUyZMiW0fZLncrmi5yTezpl/ldaSYaei3yZGvzUMO2HkLJuiKNmuAQAAABrgdicAAACS\nINgBAABIgmAHAAAgCYIdAACAJAh2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEA\nAEiCYAcAACAJgh0AAIAkHNkuAECyGhoaQtMHDhzQcGE9WKtaAJADwQ7An3OVORNVeOaLx5yV\nA4DxOBQL5LpkkhMAwBIIdoBlpDcula3RLGtVCwBy4FAsYEkNDQ0JMlDyg3DGDNdpUi2ZDwAm\nRLADchRHYAFAPhyKBawk1VGrmMs3NDQYk+o0qRYAkDxG7ACkw5gblIRaSa+JmPmV+AhAYgQ7\nwKrinbg24WhcxKeSGb0LD1jRyydzt5S0q01PgtWa+d4uAJAhgh1gMTGjVbwlNW89cWCKblHD\naiPWk/xPF1qS0woBSI9gByBl8cb8El/9momUhgnjHcANT5n6lQoAWcTFE4CFxYs7uoo5LJfM\nB/WoNtU1EOYAyI1gB1hPMukkWwkmOmlpVe2BMBO2GL0YAOQCgh2AFMRLS3qnqOiDqhpeJwsA\n0uAcO8DarHWuWKrVJn+Qd8JrcpNvFACsixE7wJJSumgg63SqdsIwF5Le+gHAchixAyCbxOf5\nkfMASIwRO8DyrJVUDK6WqygA5BSCHWBV8S4ONWeOSaPa9A6kGvOsMwAwJ4IdgBTEi1lZGTVM\n3CipDkAOItgB0JLBzzFLtVFrHbYGgFQR7AALi34KqgHDVGk/QCLVahNc8ZDeta6kOgDS46pY\nACmLl5B0jZVJNhp6IGz4w2RjftZatwAEgGQwYgdYW3g0MSCmJGgi1UeHafKosQkXiBjbm/Bx\nZABgaQQ7AKmJmaX0y5Qx71eS+GmwieczSgdAYjZFUbJdAwCzM/m9VAAAKkbsAAAAJEGwAwAA\nkATBDgAAQBIEOwAAAEkQ7AAAACRBsAMAAJAEtzsBAACQBCN2AAAAkiDYAQAASIJgBwAAIAmC\nHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJgh0AAIAk/j+6fGnjulgehwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# install.packages('effects')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "plot_model(mlm3, type = \"eff\", show.data = T, terms = c('V1pV5a','GROUP'), axis.lim= list(c(-5, 5), c(0.4, 1.3)))#,'TIMEP'))\n",
    "ggsave('V1pV5a_3Groups.png', plot = last_plot(), scale = 1, width = 20, height = 10, units = c('cm'), dpi = 300, limitsize = TRUE)\n",
    "\n",
    "# emmip(mlm3, 'WPLIG' ~ 'GROUP')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + (1 | SUBJECT)\n",
       "   Data: G3\n",
       "\n",
       "REML criterion at convergence: -25.1\n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-2.90025 -0.36438  0.03442  0.47117  2.91387 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.001418 0.03765 \n",
       " Residual             0.027463 0.16572 \n",
       "Number of obs: 54, groups:  SUBJECT, 14\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error       df t value Pr(>|t|)    \n",
       "(Intercept)  0.80859    0.04903 49.82918  16.490  < 2e-16 ***\n",
       "TIMEPBsl     0.19141    0.06531 38.78696   2.931  0.00564 ** \n",
       "TIMEPTP0     0.08383    0.06531 38.78696   1.284  0.20687    \n",
       "TIMEPTP30    0.03763    0.06531 38.78696   0.576  0.56779    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "          (Intr) TIMEPB TIMEPTP0\n",
       "TIMEPBsl  -0.719                \n",
       "TIMEPTP0  -0.719  0.540         \n",
       "TIMEPTP30 -0.719  0.540  0.540  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.00000000</td><td>0.1088836</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.13012736</td><td>0.1989454</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.71430451</td><td>0.9030166</td></tr>\n",
       "\t<tr><th scope=row>TIMEPBsl</th><td> 0.06583983</td><td>0.3181964</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP0</th><td>-0.04173930</td><td>0.2106173</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.08793912</td><td>0.1644175</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.00000000 & 0.1088836\\\\\n",
       "\t.sigma &  0.13012736 & 0.1989454\\\\\n",
       "\t(Intercept) &  0.71430451 & 0.9030166\\\\\n",
       "\tTIMEPBsl &  0.06583983 & 0.3181964\\\\\n",
       "\tTIMEPTP0 & -0.04173930 & 0.2106173\\\\\n",
       "\tTIMEPTP30 & -0.08793912 & 0.1644175\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.00000000 | 0.1088836 |\n",
       "| .sigma |  0.13012736 | 0.1989454 |\n",
       "| (Intercept) |  0.71430451 | 0.9030166 |\n",
       "| TIMEPBsl |  0.06583983 | 0.3181964 |\n",
       "| TIMEPTP0 | -0.04173930 | 0.2106173 |\n",
       "| TIMEPTP30 | -0.08793912 | 0.1644175 |\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %       97.5 %   \n",
       ".sig01       0.00000000 0.1088836\n",
       ".sigma       0.13012736 0.1989454\n",
       "(Intercept)  0.71430451 0.9030166\n",
       "TIMEPBsl     0.06583983 0.3181964\n",
       "TIMEPTP0    -0.04173930 0.2106173\n",
       "TIMEPTP30   -0.08793912 0.1644175"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + (1 | SUBJECT)\n",
       "   Data: G4\n",
       "\n",
       "REML criterion at convergence: -19.3\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.2148 -0.5897  0.0774  0.5992  3.2822 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.007647 0.08745 \n",
       " Residual             0.027541 0.16596 \n",
       "Number of obs: 57, groups:  SUBJECT, 15\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error       df t value Pr(>|t|)    \n",
       "(Intercept)  0.83123    0.04997 48.13963  16.635  < 2e-16 ***\n",
       "TIMEPBsl     0.16877    0.06183 39.99398   2.729  0.00938 ** \n",
       "TIMEPTP0     0.04525    0.06183 39.99398   0.732  0.46852    \n",
       "TIMEPTP30   -0.04130    0.06446 40.95285  -0.641  0.52531    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "          (Intr) TIMEPB TIMEPTP0\n",
       "TIMEPBsl  -0.643                \n",
       "TIMEPTP0  -0.643  0.520         \n",
       "TIMEPTP30 -0.618  0.499  0.499  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.00000000</td><td>0.15608411</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.13117255</td><td>0.20102488</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.73504657</td><td>0.92757478</td></tr>\n",
       "\t<tr><th scope=row>TIMEPBsl</th><td> 0.04940752</td><td>0.28838462</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP0</th><td>-0.07410996</td><td>0.16486714</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.16562644</td><td>0.08341061</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.00000000 & 0.15608411\\\\\n",
       "\t.sigma &  0.13117255 & 0.20102488\\\\\n",
       "\t(Intercept) &  0.73504657 & 0.92757478\\\\\n",
       "\tTIMEPBsl &  0.04940752 & 0.28838462\\\\\n",
       "\tTIMEPTP0 & -0.07410996 & 0.16486714\\\\\n",
       "\tTIMEPTP30 & -0.16562644 & 0.08341061\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.00000000 | 0.15608411 |\n",
       "| .sigma |  0.13117255 | 0.20102488 |\n",
       "| (Intercept) |  0.73504657 | 0.92757478 |\n",
       "| TIMEPBsl |  0.04940752 | 0.28838462 |\n",
       "| TIMEPTP0 | -0.07410996 | 0.16486714 |\n",
       "| TIMEPTP30 | -0.16562644 | 0.08341061 |\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %       97.5 %    \n",
       ".sig01       0.00000000 0.15608411\n",
       ".sigma       0.13117255 0.20102488\n",
       "(Intercept)  0.73504657 0.92757478\n",
       "TIMEPBsl     0.04940752 0.28838462\n",
       "TIMEPTP0    -0.07410996 0.16486714\n",
       "TIMEPTP30   -0.16562644 0.08341061"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + (1 | SUBJECT)\n",
       "   Data: G5\n",
       "\n",
       "REML criterion at convergence: -4.8\n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.94540 -0.53708  0.02758  0.64342  1.83887 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.02155  0.1468  \n",
       " Residual             0.03143  0.1773  \n",
       "Number of obs: 58, groups:  SUBJECT, 15\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error       df t value Pr(>|t|)    \n",
       "(Intercept)  0.94977    0.06096 38.60113  15.582   <2e-16 ***\n",
       "TIMEPBsl     0.05023    0.06614 40.42600   0.759    0.452    \n",
       "TIMEPTP0    -0.04671    0.06614 40.42600  -0.706    0.484    \n",
       "TIMEPTP30   -0.04251    0.06755 40.73402  -0.629    0.533    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "          (Intr) TIMEPB TIMEPTP0\n",
       "TIMEPBsl  -0.565                \n",
       "TIMEPTP0  -0.565  0.521         \n",
       "TIMEPTP30 -0.554  0.511  0.511  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.07997201</td><td>0.23407149</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.14040788</td><td>0.21456857</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.83121720</td><td>1.06757477</td></tr>\n",
       "\t<tr><th scope=row>TIMEPBsl</th><td>-0.07798236</td><td>0.17780187</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP0</th><td>-0.17492089</td><td>0.08086334</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.17326693</td><td>0.08789225</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.07997201 & 0.23407149\\\\\n",
       "\t.sigma &  0.14040788 & 0.21456857\\\\\n",
       "\t(Intercept) &  0.83121720 & 1.06757477\\\\\n",
       "\tTIMEPBsl & -0.07798236 & 0.17780187\\\\\n",
       "\tTIMEPTP0 & -0.17492089 & 0.08086334\\\\\n",
       "\tTIMEPTP30 & -0.17326693 & 0.08789225\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.07997201 | 0.23407149 |\n",
       "| .sigma |  0.14040788 | 0.21456857 |\n",
       "| (Intercept) |  0.83121720 | 1.06757477 |\n",
       "| TIMEPBsl | -0.07798236 | 0.17780187 |\n",
       "| TIMEPTP0 | -0.17492089 | 0.08086334 |\n",
       "| TIMEPTP30 | -0.17326693 | 0.08789225 |\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %       97.5 %    \n",
       ".sig01       0.07997201 0.23407149\n",
       ".sigma       0.14040788 0.21456857\n",
       "(Intercept)  0.83121720 1.06757477\n",
       "TIMEPBsl    -0.07798236 0.17780187\n",
       "TIMEPTP0    -0.17492089 0.08086334\n",
       "TIMEPTP30   -0.17326693 0.08789225"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Single GROUP evaluation over time\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "\n",
    "G3 <- ndr[which(ndr$GROUP=='aV1-gV5'), ]\n",
    "G4 <- ndr[which(ndr$GROUP=='gV1-aV5'), ]\n",
    "G5 <- ndr[which(ndr$GROUP=='Sham'), ]\n",
    "\n",
    "G3$TIMEP <- relevel(G3$TIMEP,\"TP10\")   # changed the intercept to TIMEP:TP0?\n",
    "G4$TIMEP <- relevel(G4$TIMEP,\"TP10\")   # changed the intercept to TIMEP:TP0?\n",
    "G5$TIMEP <- relevel(G5$TIMEP,\"TP10\")   # changed the intercept to TIMEP:TP0?\n",
    "\n",
    "mlm4 <- lmer(NDR ~ 1 + TIMEP + (1|SUBJECT), data=G3, REML=TRUE)\n",
    "summary(mlm4)\n",
    "confint(mlm4)\n",
    "mlm5 <- lmer(NDR ~ 1 + TIMEP + (1|SUBJECT), data=G4, REML=TRUE)\n",
    "summary(mlm5)\n",
    "confint(mlm5)\n",
    "mlm6 <- lmer(NDR ~ 1 + TIMEP + (1|SUBJECT), data=G5, REML=TRUE)\n",
    "summary(mlm6)\n",
    "confint(mlm6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>176</li><li>20</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 176\n",
       "\\item 20\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 176\n",
       "2. 20\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 176  20"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t176 obs. of  20 variables:\n",
      " $ X      : int  0 1 2 3 4 5 6 7 8 9 ...\n",
      " $ NDR    : num  41.4 29.7 21.5 12.5 39.4 ...\n",
      " $ SUBJECT: Factor w/ 44 levels \"1\",\"2\",\"3\",\"4\",..: 1 2 3 4 5 6 7 8 9 10 ...\n",
      " $ GROUP  : Factor w/ 3 levels \"aV1-gV5\",\"gV1-aV5\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ TIMEP  : Factor w/ 4 levels \"Bsl\",\"TP0\",\"TP10\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ PSDA   : num  2.86e-13 5.08e-13 4.63e-13 4.06e-13 4.20e-13 ...\n",
      " $ PSDB   : num  1.68e-13 2.29e-13 1.48e-13 2.79e-13 3.90e-13 ...\n",
      " $ PSDG   : num  1.31e-13 1.81e-13 1.46e-13 2.19e-13 1.55e-13 ...\n",
      " $ COHA   : num  0.157 0.328 0.118 0.281 0.357 ...\n",
      " $ COHB   : num  0.1234 0.2916 0.0956 0.2891 0.3165 ...\n",
      " $ COHG   : num  0.1145 0.2893 0.0954 0.2341 0.3401 ...\n",
      " $ V1pV5a : num  0.5188 2.5105 -0.7129 -0.5849 0.0852 ...\n",
      " $ V1aV5p : num  1.327 2.001 0.574 1.348 3.106 ...\n",
      " $ WPLIA  : num  0.1236 0.1468 0.0929 0.1653 0.0965 ...\n",
      " $ WPLIB  : num  0.133 0.142 0.099 0.104 0.091 ...\n",
      " $ WPLIG  : num  0.112 0.131 0.153 0.139 0.136 ...\n",
      " $ PSIT   : num  -9.87e-03 -6.25e-05 5.13e-04 -2.58e-04 1.28e-03 ...\n",
      " $ PSIA   : num  -9.87e-03 -6.25e-05 5.13e-04 -2.58e-04 1.28e-03 ...\n",
      " $ PSIB   : num  0.012581 0.010862 -0.002021 -0.000313 0.003562 ...\n",
      " $ PSIG   : num  -0.00437 -0.00674 0.00195 -0.0066 0.00171 ...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + GROUP + (1 | SUBJECT)\n",
       "   Data: ndr\n",
       "\n",
       "REML criterion at convergence: 1330.3\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.4903 -0.3473  0.0139  0.4508  2.3140 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 347.81   18.650  \n",
       " Residual              59.56    7.717  \n",
       "Number of obs: 176, groups:  SUBJECT, 44\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error      df t value Pr(>|t|)    \n",
       "(Intercept)    40.116      5.019  44.490   7.992 3.83e-10 ***\n",
       "TIMEPTP0       -5.797      1.645 129.000  -3.523  0.00059 ***\n",
       "TIMEPTP10      -6.146      1.645 129.000  -3.735  0.00028 ***\n",
       "TIMEPTP30      -7.418      1.645 129.000  -4.508 1.45e-05 ***\n",
       "GROUPaV1-gV5   -6.214      7.077  41.000  -0.878  0.38508    \n",
       "GROUPgV1-aV5    7.155      6.954  41.000   1.029  0.30954    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) TIMEPTP0 TIMEPTP1 TIMEPTP3 GROUPV1-gV5\n",
       "TIMEPTP0    -0.164                                       \n",
       "TIMEPTP10   -0.164  0.500                                \n",
       "TIMEPTP30   -0.164  0.500    0.500                       \n",
       "GROUPV1-gV5 -0.681  0.000    0.000    0.000              \n",
       "GROUPgV1-V5 -0.693  0.000    0.000    0.000    0.491     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "$`simple contrasts for TIMEP`\n",
       "GROUP = Sham:\n",
       " contrast    estimate   SE  df t.ratio p.value\n",
       " Bsl - TP0      5.797 1.65 129 3.523   0.0006 \n",
       " Bsl - TP10     6.146 1.65 129 3.735   0.0003 \n",
       " Bsl - TP30     7.418 1.65 129 4.508   <.0001 \n",
       " TP0 - TP10     0.349 1.65 129 0.212   0.8324 \n",
       " TP0 - TP30     1.621 1.65 129 0.985   0.3263 \n",
       " TP10 - TP30    1.272 1.65 129 0.773   0.4408 \n",
       "\n",
       "GROUP = aV1-gV5:\n",
       " contrast    estimate   SE  df t.ratio p.value\n",
       " Bsl - TP0      5.797 1.65 129 3.523   0.0006 \n",
       " Bsl - TP10     6.146 1.65 129 3.735   0.0003 \n",
       " Bsl - TP30     7.418 1.65 129 4.508   <.0001 \n",
       " TP0 - TP10     0.349 1.65 129 0.212   0.8324 \n",
       " TP0 - TP30     1.621 1.65 129 0.985   0.3263 \n",
       " TP10 - TP30    1.272 1.65 129 0.773   0.4408 \n",
       "\n",
       "GROUP = gV1-aV5:\n",
       " contrast    estimate   SE  df t.ratio p.value\n",
       " Bsl - TP0      5.797 1.65 129 3.523   0.0006 \n",
       " Bsl - TP10     6.146 1.65 129 3.735   0.0003 \n",
       " Bsl - TP30     7.418 1.65 129 4.508   <.0001 \n",
       " TP0 - TP10     0.349 1.65 129 0.212   0.8324 \n",
       " TP0 - TP30     1.621 1.65 129 0.985   0.3263 \n",
       " TP10 - TP30    1.272 1.65 129 0.773   0.4408 \n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       "TIMEP = Bsl:\n",
       " contrast              estimate   SE df t.ratio p.value\n",
       " Sham - (aV1-gV5)          6.21 7.08 41  0.878  0.3851 \n",
       " Sham - (gV1-aV5)         -7.16 6.95 41 -1.029  0.3095 \n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41 -1.889  0.0660 \n",
       "\n",
       "TIMEP = TP0:\n",
       " contrast              estimate   SE df t.ratio p.value\n",
       " Sham - (aV1-gV5)          6.21 7.08 41  0.878  0.3851 \n",
       " Sham - (gV1-aV5)         -7.16 6.95 41 -1.029  0.3095 \n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41 -1.889  0.0660 \n",
       "\n",
       "TIMEP = TP10:\n",
       " contrast              estimate   SE df t.ratio p.value\n",
       " Sham - (aV1-gV5)          6.21 7.08 41  0.878  0.3851 \n",
       " Sham - (gV1-aV5)         -7.16 6.95 41 -1.029  0.3095 \n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41 -1.889  0.0660 \n",
       "\n",
       "TIMEP = TP30:\n",
       " contrast              estimate   SE df t.ratio p.value\n",
       " Sham - (aV1-gV5)          6.21 7.08 41  0.878  0.3851 \n",
       " Sham - (gV1-aV5)         -7.16 6.95 41 -1.029  0.3095 \n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41 -1.889  0.0660 \n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`simple contrasts for TIMEP`</dt>\n",
       "\t\t<dd><table>\n",
       "<caption>A summary_emm: 18 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>contrast</th><th scope=col>GROUP</th><th scope=col>estimate</th><th scope=col>SE</th><th scope=col>df</th><th scope=col>lower.CL</th><th scope=col>upper.CL</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Bsl - TP0  </td><td>Sham   </td><td>5.796771</td><td>1.64533</td><td>129</td><td> 2.541444</td><td> 9.052097</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Bsl - TP10 </td><td>Sham   </td><td>6.145770</td><td>1.64533</td><td>129</td><td> 2.890443</td><td> 9.401096</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>Bsl - TP30 </td><td>Sham   </td><td>7.417865</td><td>1.64533</td><td>129</td><td> 4.162539</td><td>10.673192</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>TP0 - TP10 </td><td>Sham   </td><td>0.348999</td><td>1.64533</td><td>129</td><td>-2.906327</td><td> 3.604325</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>TP0 - TP30 </td><td>Sham   </td><td>1.621095</td><td>1.64533</td><td>129</td><td>-1.634232</td><td> 4.876421</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>TP10 - TP30</td><td>Sham   </td><td>1.272096</td><td>1.64533</td><td>129</td><td>-1.983231</td><td> 4.527422</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>Bsl - TP0  </td><td>aV1-gV5</td><td>5.796771</td><td>1.64533</td><td>129</td><td> 2.541444</td><td> 9.052097</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>Bsl - TP10 </td><td>aV1-gV5</td><td>6.145770</td><td>1.64533</td><td>129</td><td> 2.890443</td><td> 9.401096</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>Bsl - TP30 </td><td>aV1-gV5</td><td>7.417865</td><td>1.64533</td><td>129</td><td> 4.162539</td><td>10.673192</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>TP0 - TP10 </td><td>aV1-gV5</td><td>0.348999</td><td>1.64533</td><td>129</td><td>-2.906327</td><td> 3.604325</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>TP0 - TP30 </td><td>aV1-gV5</td><td>1.621095</td><td>1.64533</td><td>129</td><td>-1.634232</td><td> 4.876421</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>TP10 - TP30</td><td>aV1-gV5</td><td>1.272096</td><td>1.64533</td><td>129</td><td>-1.983231</td><td> 4.527422</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>Bsl - TP0  </td><td>gV1-aV5</td><td>5.796771</td><td>1.64533</td><td>129</td><td> 2.541444</td><td> 9.052097</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>Bsl - TP10 </td><td>gV1-aV5</td><td>6.145770</td><td>1.64533</td><td>129</td><td> 2.890443</td><td> 9.401096</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>Bsl - TP30 </td><td>gV1-aV5</td><td>7.417865</td><td>1.64533</td><td>129</td><td> 4.162539</td><td>10.673192</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>TP0 - TP10 </td><td>gV1-aV5</td><td>0.348999</td><td>1.64533</td><td>129</td><td>-2.906327</td><td> 3.604325</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>TP0 - TP30 </td><td>gV1-aV5</td><td>1.621095</td><td>1.64533</td><td>129</td><td>-1.634232</td><td> 4.876421</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>TP10 - TP30</td><td>gV1-aV5</td><td>1.272096</td><td>1.64533</td><td>129</td><td>-1.983231</td><td> 4.527422</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$`simple contrasts for GROUP`</dt>\n",
       "\t\t<dd><table>\n",
       "<caption>A summary_emm: 12 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>contrast</th><th scope=col>TIMEP</th><th scope=col>estimate</th><th scope=col>SE</th><th scope=col>df</th><th scope=col>lower.CL</th><th scope=col>upper.CL</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Sham - (aV1-gV5)     </td><td>Bsl </td><td>  6.213547</td><td>7.077244</td><td>41</td><td> -8.079237</td><td>20.5063322</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Sham - (gV1-aV5)     </td><td>Bsl </td><td> -7.155370</td><td>6.954152</td><td>41</td><td>-21.199566</td><td> 6.8888255</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>(aV1-gV5) - (gV1-aV5)</td><td>Bsl </td><td>-13.368918</td><td>7.077244</td><td>41</td><td>-27.661702</td><td> 0.9238671</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>Sham - (aV1-gV5)     </td><td>TP0 </td><td>  6.213547</td><td>7.077244</td><td>41</td><td> -8.079237</td><td>20.5063322</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>Sham - (gV1-aV5)     </td><td>TP0 </td><td> -7.155370</td><td>6.954152</td><td>41</td><td>-21.199566</td><td> 6.8888255</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>(aV1-gV5) - (gV1-aV5)</td><td>TP0 </td><td>-13.368918</td><td>7.077244</td><td>41</td><td>-27.661702</td><td> 0.9238671</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>Sham - (aV1-gV5)     </td><td>TP10</td><td>  6.213547</td><td>7.077244</td><td>41</td><td> -8.079237</td><td>20.5063322</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>Sham - (gV1-aV5)     </td><td>TP10</td><td> -7.155370</td><td>6.954152</td><td>41</td><td>-21.199566</td><td> 6.8888255</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>(aV1-gV5) - (gV1-aV5)</td><td>TP10</td><td>-13.368918</td><td>7.077244</td><td>41</td><td>-27.661702</td><td> 0.9238671</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>Sham - (aV1-gV5)     </td><td>TP30</td><td>  6.213547</td><td>7.077244</td><td>41</td><td> -8.079237</td><td>20.5063322</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>Sham - (gV1-aV5)     </td><td>TP30</td><td> -7.155370</td><td>6.954152</td><td>41</td><td>-21.199566</td><td> 6.8888255</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>(aV1-gV5) - (gV1-aV5)</td><td>TP30</td><td>-13.368918</td><td>7.077244</td><td>41</td><td>-27.661702</td><td> 0.9238671</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`simple contrasts for TIMEP`] A summary\\_emm: 18 × 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       "  & contrast & GROUP & estimate & SE & df & lower.CL & upper.CL\\\\\n",
       "  & <fct> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Bsl - TP0   & Sham    & 5.796771 & 1.64533 & 129 &  2.541444 &  9.052097\\\\\n",
       "\t2 & Bsl - TP10  & Sham    & 6.145770 & 1.64533 & 129 &  2.890443 &  9.401096\\\\\n",
       "\t3 & Bsl - TP30  & Sham    & 7.417865 & 1.64533 & 129 &  4.162539 & 10.673192\\\\\n",
       "\t4 & TP0 - TP10  & Sham    & 0.348999 & 1.64533 & 129 & -2.906327 &  3.604325\\\\\n",
       "\t5 & TP0 - TP30  & Sham    & 1.621095 & 1.64533 & 129 & -1.634232 &  4.876421\\\\\n",
       "\t6 & TP10 - TP30 & Sham    & 1.272096 & 1.64533 & 129 & -1.983231 &  4.527422\\\\\n",
       "\t7 & Bsl - TP0   & aV1-gV5 & 5.796771 & 1.64533 & 129 &  2.541444 &  9.052097\\\\\n",
       "\t8 & Bsl - TP10  & aV1-gV5 & 6.145770 & 1.64533 & 129 &  2.890443 &  9.401096\\\\\n",
       "\t9 & Bsl - TP30  & aV1-gV5 & 7.417865 & 1.64533 & 129 &  4.162539 & 10.673192\\\\\n",
       "\t10 & TP0 - TP10  & aV1-gV5 & 0.348999 & 1.64533 & 129 & -2.906327 &  3.604325\\\\\n",
       "\t11 & TP0 - TP30  & aV1-gV5 & 1.621095 & 1.64533 & 129 & -1.634232 &  4.876421\\\\\n",
       "\t12 & TP10 - TP30 & aV1-gV5 & 1.272096 & 1.64533 & 129 & -1.983231 &  4.527422\\\\\n",
       "\t13 & Bsl - TP0   & gV1-aV5 & 5.796771 & 1.64533 & 129 &  2.541444 &  9.052097\\\\\n",
       "\t14 & Bsl - TP10  & gV1-aV5 & 6.145770 & 1.64533 & 129 &  2.890443 &  9.401096\\\\\n",
       "\t15 & Bsl - TP30  & gV1-aV5 & 7.417865 & 1.64533 & 129 &  4.162539 & 10.673192\\\\\n",
       "\t16 & TP0 - TP10  & gV1-aV5 & 0.348999 & 1.64533 & 129 & -2.906327 &  3.604325\\\\\n",
       "\t17 & TP0 - TP30  & gV1-aV5 & 1.621095 & 1.64533 & 129 & -1.634232 &  4.876421\\\\\n",
       "\t18 & TP10 - TP30 & gV1-aV5 & 1.272096 & 1.64533 & 129 & -1.983231 &  4.527422\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$`simple contrasts for GROUP`] A summary\\_emm: 12 × 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       "  & contrast & TIMEP & estimate & SE & df & lower.CL & upper.CL\\\\\n",
       "  & <fct> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Sham - (aV1-gV5)      & Bsl  &   6.213547 & 7.077244 & 41 &  -8.079237 & 20.5063322\\\\\n",
       "\t2 & Sham - (gV1-aV5)      & Bsl  &  -7.155370 & 6.954152 & 41 & -21.199566 &  6.8888255\\\\\n",
       "\t3 & (aV1-gV5) - (gV1-aV5) & Bsl  & -13.368918 & 7.077244 & 41 & -27.661702 &  0.9238671\\\\\n",
       "\t4 & Sham - (aV1-gV5)      & TP0  &   6.213547 & 7.077244 & 41 &  -8.079237 & 20.5063322\\\\\n",
       "\t5 & Sham - (gV1-aV5)      & TP0  &  -7.155370 & 6.954152 & 41 & -21.199566 &  6.8888255\\\\\n",
       "\t6 & (aV1-gV5) - (gV1-aV5) & TP0  & -13.368918 & 7.077244 & 41 & -27.661702 &  0.9238671\\\\\n",
       "\t7 & Sham - (aV1-gV5)      & TP10 &   6.213547 & 7.077244 & 41 &  -8.079237 & 20.5063322\\\\\n",
       "\t8 & Sham - (gV1-aV5)      & TP10 &  -7.155370 & 6.954152 & 41 & -21.199566 &  6.8888255\\\\\n",
       "\t9 & (aV1-gV5) - (gV1-aV5) & TP10 & -13.368918 & 7.077244 & 41 & -27.661702 &  0.9238671\\\\\n",
       "\t10 & Sham - (aV1-gV5)      & TP30 &   6.213547 & 7.077244 & 41 &  -8.079237 & 20.5063322\\\\\n",
       "\t11 & Sham - (gV1-aV5)      & TP30 &  -7.155370 & 6.954152 & 41 & -21.199566 &  6.8888255\\\\\n",
       "\t12 & (aV1-gV5) - (gV1-aV5) & TP30 & -13.368918 & 7.077244 & 41 & -27.661702 &  0.9238671\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`simple contrasts for TIMEP`\n",
       ":   \n",
       "A summary_emm: 18 × 7\n",
       "\n",
       "| <!--/--> | contrast &lt;fct&gt; | GROUP &lt;fct&gt; | estimate &lt;dbl&gt; | SE &lt;dbl&gt; | df &lt;dbl&gt; | lower.CL &lt;dbl&gt; | upper.CL &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 1 | Bsl - TP0   | Sham    | 5.796771 | 1.64533 | 129 |  2.541444 |  9.052097 |\n",
       "| 2 | Bsl - TP10  | Sham    | 6.145770 | 1.64533 | 129 |  2.890443 |  9.401096 |\n",
       "| 3 | Bsl - TP30  | Sham    | 7.417865 | 1.64533 | 129 |  4.162539 | 10.673192 |\n",
       "| 4 | TP0 - TP10  | Sham    | 0.348999 | 1.64533 | 129 | -2.906327 |  3.604325 |\n",
       "| 5 | TP0 - TP30  | Sham    | 1.621095 | 1.64533 | 129 | -1.634232 |  4.876421 |\n",
       "| 6 | TP10 - TP30 | Sham    | 1.272096 | 1.64533 | 129 | -1.983231 |  4.527422 |\n",
       "| 7 | Bsl - TP0   | aV1-gV5 | 5.796771 | 1.64533 | 129 |  2.541444 |  9.052097 |\n",
       "| 8 | Bsl - TP10  | aV1-gV5 | 6.145770 | 1.64533 | 129 |  2.890443 |  9.401096 |\n",
       "| 9 | Bsl - TP30  | aV1-gV5 | 7.417865 | 1.64533 | 129 |  4.162539 | 10.673192 |\n",
       "| 10 | TP0 - TP10  | aV1-gV5 | 0.348999 | 1.64533 | 129 | -2.906327 |  3.604325 |\n",
       "| 11 | TP0 - TP30  | aV1-gV5 | 1.621095 | 1.64533 | 129 | -1.634232 |  4.876421 |\n",
       "| 12 | TP10 - TP30 | aV1-gV5 | 1.272096 | 1.64533 | 129 | -1.983231 |  4.527422 |\n",
       "| 13 | Bsl - TP0   | gV1-aV5 | 5.796771 | 1.64533 | 129 |  2.541444 |  9.052097 |\n",
       "| 14 | Bsl - TP10  | gV1-aV5 | 6.145770 | 1.64533 | 129 |  2.890443 |  9.401096 |\n",
       "| 15 | Bsl - TP30  | gV1-aV5 | 7.417865 | 1.64533 | 129 |  4.162539 | 10.673192 |\n",
       "| 16 | TP0 - TP10  | gV1-aV5 | 0.348999 | 1.64533 | 129 | -2.906327 |  3.604325 |\n",
       "| 17 | TP0 - TP30  | gV1-aV5 | 1.621095 | 1.64533 | 129 | -1.634232 |  4.876421 |\n",
       "| 18 | TP10 - TP30 | gV1-aV5 | 1.272096 | 1.64533 | 129 | -1.983231 |  4.527422 |\n",
       "\n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       ":   \n",
       "A summary_emm: 12 × 7\n",
       "\n",
       "| <!--/--> | contrast &lt;fct&gt; | TIMEP &lt;fct&gt; | estimate &lt;dbl&gt; | SE &lt;dbl&gt; | df &lt;dbl&gt; | lower.CL &lt;dbl&gt; | upper.CL &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 1 | Sham - (aV1-gV5)      | Bsl  |   6.213547 | 7.077244 | 41 |  -8.079237 | 20.5063322 |\n",
       "| 2 | Sham - (gV1-aV5)      | Bsl  |  -7.155370 | 6.954152 | 41 | -21.199566 |  6.8888255 |\n",
       "| 3 | (aV1-gV5) - (gV1-aV5) | Bsl  | -13.368918 | 7.077244 | 41 | -27.661702 |  0.9238671 |\n",
       "| 4 | Sham - (aV1-gV5)      | TP0  |   6.213547 | 7.077244 | 41 |  -8.079237 | 20.5063322 |\n",
       "| 5 | Sham - (gV1-aV5)      | TP0  |  -7.155370 | 6.954152 | 41 | -21.199566 |  6.8888255 |\n",
       "| 6 | (aV1-gV5) - (gV1-aV5) | TP0  | -13.368918 | 7.077244 | 41 | -27.661702 |  0.9238671 |\n",
       "| 7 | Sham - (aV1-gV5)      | TP10 |   6.213547 | 7.077244 | 41 |  -8.079237 | 20.5063322 |\n",
       "| 8 | Sham - (gV1-aV5)      | TP10 |  -7.155370 | 6.954152 | 41 | -21.199566 |  6.8888255 |\n",
       "| 9 | (aV1-gV5) - (gV1-aV5) | TP10 | -13.368918 | 7.077244 | 41 | -27.661702 |  0.9238671 |\n",
       "| 10 | Sham - (aV1-gV5)      | TP30 |   6.213547 | 7.077244 | 41 |  -8.079237 | 20.5063322 |\n",
       "| 11 | Sham - (gV1-aV5)      | TP30 |  -7.155370 | 6.954152 | 41 | -21.199566 |  6.8888255 |\n",
       "| 12 | (aV1-gV5) - (gV1-aV5) | TP30 | -13.368918 | 7.077244 | 41 | -27.661702 |  0.9238671 |\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`simple contrasts for TIMEP`\n",
       "GROUP = Sham:\n",
       " contrast    estimate   SE  df lower.CL upper.CL\n",
       " Bsl - TP0      5.797 1.65 129     2.54     9.05\n",
       " Bsl - TP10     6.146 1.65 129     2.89     9.40\n",
       " Bsl - TP30     7.418 1.65 129     4.16    10.67\n",
       " TP0 - TP10     0.349 1.65 129    -2.91     3.60\n",
       " TP0 - TP30     1.621 1.65 129    -1.63     4.88\n",
       " TP10 - TP30    1.272 1.65 129    -1.98     4.53\n",
       "\n",
       "GROUP = aV1-gV5:\n",
       " contrast    estimate   SE  df lower.CL upper.CL\n",
       " Bsl - TP0      5.797 1.65 129     2.54     9.05\n",
       " Bsl - TP10     6.146 1.65 129     2.89     9.40\n",
       " Bsl - TP30     7.418 1.65 129     4.16    10.67\n",
       " TP0 - TP10     0.349 1.65 129    -2.91     3.60\n",
       " TP0 - TP30     1.621 1.65 129    -1.63     4.88\n",
       " TP10 - TP30    1.272 1.65 129    -1.98     4.53\n",
       "\n",
       "GROUP = gV1-aV5:\n",
       " contrast    estimate   SE  df lower.CL upper.CL\n",
       " Bsl - TP0      5.797 1.65 129     2.54     9.05\n",
       " Bsl - TP10     6.146 1.65 129     2.89     9.40\n",
       " Bsl - TP30     7.418 1.65 129     4.16    10.67\n",
       " TP0 - TP10     0.349 1.65 129    -2.91     3.60\n",
       " TP0 - TP30     1.621 1.65 129    -1.63     4.88\n",
       " TP10 - TP30    1.272 1.65 129    -1.98     4.53\n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "Confidence level used: 0.95 \n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       "TIMEP = Bsl:\n",
       " contrast              estimate   SE df lower.CL upper.CL\n",
       " Sham - (aV1-gV5)          6.21 7.08 41    -8.08   20.506\n",
       " Sham - (gV1-aV5)         -7.16 6.95 41   -21.20    6.889\n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41   -27.66    0.924\n",
       "\n",
       "TIMEP = TP0:\n",
       " contrast              estimate   SE df lower.CL upper.CL\n",
       " Sham - (aV1-gV5)          6.21 7.08 41    -8.08   20.506\n",
       " Sham - (gV1-aV5)         -7.16 6.95 41   -21.20    6.889\n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41   -27.66    0.924\n",
       "\n",
       "TIMEP = TP10:\n",
       " contrast              estimate   SE df lower.CL upper.CL\n",
       " Sham - (aV1-gV5)          6.21 7.08 41    -8.08   20.506\n",
       " Sham - (gV1-aV5)         -7.16 6.95 41   -21.20    6.889\n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41   -27.66    0.924\n",
       "\n",
       "TIMEP = TP30:\n",
       " contrast              estimate   SE df lower.CL upper.CL\n",
       " Sham - (aV1-gV5)          6.21 7.08 41    -8.08   20.506\n",
       " Sham - (gV1-aV5)         -7.16 6.95 41   -21.20    6.889\n",
       " (aV1-gV5) - (gV1-aV5)   -13.37 7.08 41   -27.66    0.924\n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "Confidence level used: 0.95 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Raw dataset. Is the baseline different and comparable between groups? YESSSSS!\n",
    "\n",
    "library(simr)\n",
    "library(Matrix)\n",
    "library(lme4)\n",
    "library(emmeans)\n",
    "library(lattice)## LOADING AND INSPECTING THE DATA\n",
    "library(lmerTest) ## INFERENTIAL TESTS\n",
    "# install.packages('mice')\n",
    "library(mice)\n",
    "library(ggplot2)\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_All_Raw.txt',header=TRUE,sep='\\t')\n",
    "# ndr[45:88,]\n",
    "dim(ndr)\n",
    "\n",
    "## SIMPLE PLOTS\n",
    "plot(NDR~TIMEP,data=ndr,col=\"grey50\",pch=\"+\")\n",
    "# xyplot(NDR~TIMEP,groups=GROUP,data=ndr,pch=\"+\",cex=1.5)\n",
    "\n",
    "## TURN NUMERICAL VALUES INTO FACTOR/CATEGORICAL VARIABLES\n",
    "ndr$TIMEP <- factor(ndr$TIMEP)\n",
    "ndr$GROUP <- factor(ndr$GROUP)\n",
    "ndr$SUBJECT <- factor(ndr$SUBJECT)\n",
    "str(ndr)\n",
    "\n",
    "## RANDOM INTERCEPT MODEL\n",
    "ndr$TIMEP <- relevel(ndr$TIMEP,\"Bsl\")   # changed the intercept to TIMEP:TP0\n",
    "ndr$GROUP <- relevel(ndr$GROUP,\"Sham\")   # changed the intercept to GROUP:Sham\n",
    "mlm1 <- lmer(NDR ~ 1 + TIMEP + GROUP + (1|SUBJECT), data=ndr, REML=TRUE)#, na.action=\"na.fail\")\n",
    "summary(mlm1)\n",
    "emm = emmeans(mlm1, ~ TIMEP + GROUP, ddf=\"Kenward-Roger\")\n",
    "pairs(emm, simple='each', adjust=\"none\")\n",
    "confint(pairs(emm, simple='each', adjust=\"none\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + GROUP * WPLIA + (1 | SUBJECT)\n",
       "   Data: ndr\n",
       "\n",
       "REML criterion at convergence: -58.7\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.0621 -0.3314 -0.0333  0.3618  3.8453 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.003695 0.06079 \n",
       " Residual             0.016653 0.12905 \n",
       "Number of obs: 72, groups:  SUBJECT, 29\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error       df t value Pr(>|t|)    \n",
       "(Intercept)         0.94273    0.12676 65.83496   7.437 2.73e-10 ***\n",
       "TIMEPTP10          -0.13833    0.03897 49.32241  -3.550 0.000858 ***\n",
       "TIMEPTP30          -0.18210    0.03661 47.91072  -4.974 8.84e-06 ***\n",
       "GROUPgV1-aV5       -0.34718    0.16636 64.60647  -2.087 0.040846 *  \n",
       "WPLIA               0.06165    0.12536 65.99989   0.492 0.624520    \n",
       "GROUPgV1-aV5:WPLIA  0.33871    0.16802 65.68951   2.016 0.047900 *  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) TIMEPTP1 TIMEPTP3 GROUPgV1-V5 WPLIA \n",
       "TIMEPTP10   -0.274                                     \n",
       "TIMEPTP30   -0.218  0.427                              \n",
       "GROUPgV1-V5 -0.709  0.021    0.073                     \n",
       "WPLIA       -0.965  0.160    0.103    0.705            \n",
       "GROUPV1-V5:  0.699 -0.021   -0.084   -0.973      -0.733"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 8 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.00000000</td><td> 0.10002080</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.10288371</td><td> 0.15423587</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.70195616</td><td> 1.18410341</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP10</th><td>-0.21295135</td><td>-0.06316277</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.25256607</td><td>-0.11176347</td></tr>\n",
       "\t<tr><th scope=row>GROUPgV1-aV5</th><td>-0.66647887</td><td>-0.03025611</td></tr>\n",
       "\t<tr><th scope=row>WPLIA</th><td>-0.17739780</td><td> 0.29976490</td></tr>\n",
       "\t<tr><th scope=row>GROUPgV1-aV5:WPLIA</th><td> 0.01868658</td><td> 0.66240191</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 8 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.00000000 &  0.10002080\\\\\n",
       "\t.sigma &  0.10288371 &  0.15423587\\\\\n",
       "\t(Intercept) &  0.70195616 &  1.18410341\\\\\n",
       "\tTIMEPTP10 & -0.21295135 & -0.06316277\\\\\n",
       "\tTIMEPTP30 & -0.25256607 & -0.11176347\\\\\n",
       "\tGROUPgV1-aV5 & -0.66647887 & -0.03025611\\\\\n",
       "\tWPLIA & -0.17739780 &  0.29976490\\\\\n",
       "\tGROUPgV1-aV5:WPLIA &  0.01868658 &  0.66240191\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 8 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.00000000 |  0.10002080 |\n",
       "| .sigma |  0.10288371 |  0.15423587 |\n",
       "| (Intercept) |  0.70195616 |  1.18410341 |\n",
       "| TIMEPTP10 | -0.21295135 | -0.06316277 |\n",
       "| TIMEPTP30 | -0.25256607 | -0.11176347 |\n",
       "| GROUPgV1-aV5 | -0.66647887 | -0.03025611 |\n",
       "| WPLIA | -0.17739780 |  0.29976490 |\n",
       "| GROUPgV1-aV5:WPLIA |  0.01868658 |  0.66240191 |\n",
       "\n"
      ],
      "text/plain": [
       "                   2.5 %       97.5 %     \n",
       ".sig01              0.00000000  0.10002080\n",
       ".sigma              0.10288371  0.15423587\n",
       "(Intercept)         0.70195616  1.18410341\n",
       "TIMEPTP10          -0.21295135 -0.06316277\n",
       "TIMEPTP30          -0.25256607 -0.11176347\n",
       "GROUPgV1-aV5       -0.66647887 -0.03025611\n",
       "WPLIA              -0.17739780  0.29976490\n",
       "GROUPgV1-aV5:WPLIA  0.01868658  0.66240191"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>NumDF</th><th scope=col>DenDF</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>TIMEP</th><td>0.45350119</td><td>0.22675059</td><td>2</td><td>48.52196</td><td>13.615998</td><td>2.024423e-05</td></tr>\n",
       "\t<tr><th scope=row>GROUP</th><td>0.07252876</td><td>0.07252876</td><td>1</td><td>64.60647</td><td> 4.355232</td><td>4.084577e-02</td></tr>\n",
       "\t<tr><th scope=row>WPLIA</th><td>0.14399076</td><td>0.14399076</td><td>1</td><td>65.54380</td><td> 8.646407</td><td>4.523607e-03</td></tr>\n",
       "\t<tr><th scope=row>GROUP:WPLIA</th><td>0.06767890</td><td>0.06767890</td><td>1</td><td>65.68951</td><td> 4.064006</td><td>4.789977e-02</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Sum Sq & Mean Sq & NumDF & DenDF & F value & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tTIMEP & 0.45350119 & 0.22675059 & 2 & 48.52196 & 13.615998 & 2.024423e-05\\\\\n",
       "\tGROUP & 0.07252876 & 0.07252876 & 1 & 64.60647 &  4.355232 & 4.084577e-02\\\\\n",
       "\tWPLIA & 0.14399076 & 0.14399076 & 1 & 65.54380 &  8.646407 & 4.523607e-03\\\\\n",
       "\tGROUP:WPLIA & 0.06767890 & 0.06767890 & 1 & 65.68951 &  4.064006 & 4.789977e-02\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 6\n",
       "\n",
       "| <!--/--> | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | NumDF &lt;int&gt; | DenDF &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| TIMEP | 0.45350119 | 0.22675059 | 2 | 48.52196 | 13.615998 | 2.024423e-05 |\n",
       "| GROUP | 0.07252876 | 0.07252876 | 1 | 64.60647 |  4.355232 | 4.084577e-02 |\n",
       "| WPLIA | 0.14399076 | 0.14399076 | 1 | 65.54380 |  8.646407 | 4.523607e-03 |\n",
       "| GROUP:WPLIA | 0.06767890 | 0.06767890 | 1 | 65.68951 |  4.064006 | 4.789977e-02 |\n",
       "\n"
      ],
      "text/plain": [
       "            Sum Sq     Mean Sq    NumDF DenDF    F value   Pr(>F)      \n",
       "TIMEP       0.45350119 0.22675059 2     48.52196 13.615998 2.024423e-05\n",
       "GROUP       0.07252876 0.07252876 1     64.60647  4.355232 4.084577e-02\n",
       "WPLIA       0.14399076 0.14399076 1     65.54380  8.646407 4.523607e-03\n",
       "GROUP:WPLIA 0.06767890 0.06767890 1     65.68951  4.064006 4.789977e-02"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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XK5XK6npycSiTi9FlspijI/P9/f39/K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\niV+ricTk1FTd+4YikeqTGGIxORaX1gzasHJAFwqFaiSO8WByye4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4WPLXmYMLBeWbOw+/mswKIbrbw7dfe/7G0fq7J32AqgPM0tzUYtfG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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Difference between Verum groups\n",
    "\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "\n",
    "ndr$GROUP <- relevel(ndr$GROUP,\"aV1-gV5\")   # changed the intercept to GROUP\n",
    "ndr$TIMEP <- relevel(ndr$TIMEP,\"Bsl\")   # changed the intercept to GROUP\n",
    "ndr <- ndr[!(ndr$GROUP==\"Sham\"),] # drop all data from Sham\n",
    "\n",
    "mlm4 <- lmer(NDR ~ 1 + TIMEP+GROUP*WPLIA + (1|SUBJECT), data=ndr, REML=TRUE)#, na.action=\"na.fail\")\n",
    "summary(mlm4)\n",
    "confint(mlm4)\n",
    "anova(mlm4, type=2)\n",
    "plot_model(mlm4, type = \"pred\", terms = c(\"WPLIA\", \"GROUP\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Scale for 'y' is already present. Adding another scale for 'y', which will\n",
      "replace the existing scale.\n",
      "\n",
      "Warning message:\n",
      "“Removed 5 rows containing missing values (geom_point).”\n",
      "Warning message:\n",
      "“Removed 6 row(s) containing missing values (geom_path).”\n",
      "Warning message:\n",
      "“Removed 5 rows containing missing values (geom_point).”\n",
      "Warning message:\n",
      "“Removed 6 row(s) containing missing values (geom_path).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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x/+sKPPDsAObFh1bSadYFAHdDfbhZ0sy9ls1pzn6uvrkySp4oM9PT09PT3mLACA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W44ecdXLgy/pFEHAICJCHZWZ4VIJ8OkukhRjbryotx7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\nAAAogmAHAACgCIIdAACAIgh2AAAAivj/WgOXS5G2v3AAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Correlation graphs 2 Verum groups against each other\n",
    "\n",
    "# install.packages('effects')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "plot_model(mlm4, type = \"eff\", show.data = T, terms = c('WPLIA','GROUP'), axis.lim= list(c(0.5,1.5), c(0.5, 1.3)))#,'TIMEP'))\n",
    "ggsave('WPLIA_2Groups.png', plot = last_plot(), scale = 1, width = 20, height = 10, units = c('cm'), dpi = 300, limitsize = TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'aV1-gV5'</li><li>'gV1-aV5'</li><li>'Sham'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'aV1-gV5'\n",
       "\\item 'gV1-aV5'\n",
       "\\item 'Sham'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'aV1-gV5'\n",
       "2. 'gV1-aV5'\n",
       "3. 'Sham'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"aV1-gV5\" \"gV1-aV5\" \"Sham\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'Verum'</li><li>'Sham'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Verum'\n",
       "\\item 'Sham'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Verum'\n",
       "2. 'Sham'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Verum\" \"Sham\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 22 rows containing non-finite values (stat_summary).”\n",
      "Warning message:\n",
      "“Removed 22 rows containing non-finite values (stat_compare_means).”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + TIMEP + GROUP * WPLIG + (1 | SUBJECT)\n",
       "   Data: ndr\n",
       "\n",
       "REML criterion at convergence: -67.7\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.0671 -0.4631  0.0291  0.4476  3.8079 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.006409 0.08006 \n",
       " Residual             0.021576 0.14689 \n",
       "Number of obs: 111, groups:  SUBJECT, 44\n",
       "\n",
       "Fixed effects:\n",
       "                 Estimate Std. Error        df t value Pr(>|t|)    \n",
       "(Intercept)       0.55965    0.17071 102.57557   3.278 0.001426 ** \n",
       "TIMEPTP10        -0.10262    0.03511  74.58875  -2.923 0.004588 ** \n",
       "TIMEPTP30        -0.12621    0.03405  73.76832  -3.706 0.000404 ***\n",
       "GROUPSham         0.93329    0.21514 103.30805   4.338 3.35e-05 ***\n",
       "WPLIG             0.41563    0.16963 101.97689   2.450 0.015981 *  \n",
       "GROUPSham:WPLIG  -0.86080    0.21304 101.75674  -4.041 0.000104 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) TIMEPTP1 TIMEPTP3 GROUPSh WPLIG \n",
       "TIMEPTP10   -0.283                                 \n",
       "TIMEPTP30   -0.100  0.420                          \n",
       "GROUPSham   -0.776  0.163    0.053                 \n",
       "WPLIG       -0.986  0.207    0.015    0.770        \n",
       "GROUPS:WPLI  0.787 -0.177   -0.052   -0.983  -0.796"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 8 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.02567752</td><td> 0.11781456</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.12253681</td><td> 0.17032649</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.23050733</td><td> 0.88782206</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP10</th><td>-0.17030955</td><td>-0.03440432</td></tr>\n",
       "\t<tr><th scope=row>TIMEPTP30</th><td>-0.19182245</td><td>-0.05995758</td></tr>\n",
       "\t<tr><th scope=row>GROUPSham</th><td> 0.51890867</td><td> 1.35157766</td></tr>\n",
       "\t<tr><th scope=row>WPLIG</th><td> 0.08947498</td><td> 0.74261019</td></tr>\n",
       "\t<tr><th scope=row>GROUPSham:WPLIG</th><td>-1.27453727</td><td>-0.45090340</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 8 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.02567752 &  0.11781456\\\\\n",
       "\t.sigma &  0.12253681 &  0.17032649\\\\\n",
       "\t(Intercept) &  0.23050733 &  0.88782206\\\\\n",
       "\tTIMEPTP10 & -0.17030955 & -0.03440432\\\\\n",
       "\tTIMEPTP30 & -0.19182245 & -0.05995758\\\\\n",
       "\tGROUPSham &  0.51890867 &  1.35157766\\\\\n",
       "\tWPLIG &  0.08947498 &  0.74261019\\\\\n",
       "\tGROUPSham:WPLIG & -1.27453727 & -0.45090340\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 8 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.02567752 |  0.11781456 |\n",
       "| .sigma |  0.12253681 |  0.17032649 |\n",
       "| (Intercept) |  0.23050733 |  0.88782206 |\n",
       "| TIMEPTP10 | -0.17030955 | -0.03440432 |\n",
       "| TIMEPTP30 | -0.19182245 | -0.05995758 |\n",
       "| GROUPSham |  0.51890867 |  1.35157766 |\n",
       "| WPLIG |  0.08947498 |  0.74261019 |\n",
       "| GROUPSham:WPLIG | -1.27453727 | -0.45090340 |\n",
       "\n"
      ],
      "text/plain": [
       "                2.5 %       97.5 %     \n",
       ".sig01           0.02567752  0.11781456\n",
       ".sigma           0.12253681  0.17032649\n",
       "(Intercept)      0.23050733  0.88782206\n",
       "TIMEPTP10       -0.17030955 -0.03440432\n",
       "TIMEPTP30       -0.19182245 -0.05995758\n",
       "GROUPSham        0.51890867  1.35157766\n",
       "WPLIG            0.08947498  0.74261019\n",
       "GROUPSham:WPLIG -1.27453727 -0.45090340"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>NumDF</th><th scope=col>DenDF</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>TIMEP</th><td>0.3453402</td><td>0.1726701</td><td>2</td><td> 74.54516</td><td> 8.002972</td><td>7.102725e-04</td></tr>\n",
       "\t<tr><th scope=row>GROUP</th><td>0.4060465</td><td>0.4060465</td><td>1</td><td>103.30805</td><td>18.819583</td><td>3.352981e-05</td></tr>\n",
       "\t<tr><th scope=row>WPLIG</th><td>0.0335297</td><td>0.0335297</td><td>1</td><td>102.06516</td><td> 1.554046</td><td>2.153926e-01</td></tr>\n",
       "\t<tr><th scope=row>GROUP:WPLIG</th><td>0.3522445</td><td>0.3522445</td><td>1</td><td>101.75674</td><td>16.325947</td><td>1.037002e-04</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Sum Sq & Mean Sq & NumDF & DenDF & F value & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tTIMEP & 0.3453402 & 0.1726701 & 2 &  74.54516 &  8.002972 & 7.102725e-04\\\\\n",
       "\tGROUP & 0.4060465 & 0.4060465 & 1 & 103.30805 & 18.819583 & 3.352981e-05\\\\\n",
       "\tWPLIG & 0.0335297 & 0.0335297 & 1 & 102.06516 &  1.554046 & 2.153926e-01\\\\\n",
       "\tGROUP:WPLIG & 0.3522445 & 0.3522445 & 1 & 101.75674 & 16.325947 & 1.037002e-04\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 6\n",
       "\n",
       "| <!--/--> | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | NumDF &lt;int&gt; | DenDF &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| TIMEP | 0.3453402 | 0.1726701 | 2 |  74.54516 |  8.002972 | 7.102725e-04 |\n",
       "| GROUP | 0.4060465 | 0.4060465 | 1 | 103.30805 | 18.819583 | 3.352981e-05 |\n",
       "| WPLIG | 0.0335297 | 0.0335297 | 1 | 102.06516 |  1.554046 | 2.153926e-01 |\n",
       "| GROUP:WPLIG | 0.3522445 | 0.3522445 | 1 | 101.75674 | 16.325947 | 1.037002e-04 |\n",
       "\n"
      ],
      "text/plain": [
       "            Sum Sq    Mean Sq   NumDF DenDF     F value   Pr(>F)      \n",
       "TIMEP       0.3453402 0.1726701 2      74.54516  8.002972 7.102725e-04\n",
       "GROUP       0.4060465 0.4060465 1     103.30805 18.819583 3.352981e-05\n",
       "WPLIG       0.0335297 0.0335297 1     102.06516  1.554046 2.153926e-01\n",
       "GROUP:WPLIG 0.3522445 0.3522445 1     101.75674 16.325947 1.037002e-04"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "$`simple contrasts for TIMEP`\n",
       "GROUP = Verum:\n",
       " contrast    estimate     SE   df t.ratio p.value\n",
       " Bsl - TP10    0.1026 0.0352 71.3 2.914   0.0048 \n",
       " Bsl - TP30    0.1262 0.0341 70.4 3.697   0.0004 \n",
       " TP10 - TP30   0.0236 0.0374 72.2 0.631   0.5303 \n",
       "\n",
       "GROUP = Sham:\n",
       " contrast    estimate     SE   df t.ratio p.value\n",
       " Bsl - TP10    0.1026 0.0352 71.3 2.914   0.0048 \n",
       " Bsl - TP30    0.1262 0.0341 70.4 3.697   0.0004 \n",
       " TP10 - TP30   0.0236 0.0374 72.2 0.631   0.5303 \n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       "TIMEP = Bsl:\n",
       " contrast     estimate     SE   df t.ratio p.value\n",
       " Verum - Sham  -0.0787 0.0394 39.8 -1.998  0.0526 \n",
       "\n",
       "TIMEP = TP10:\n",
       " contrast     estimate     SE   df t.ratio p.value\n",
       " Verum - Sham  -0.0787 0.0394 39.8 -1.998  0.0526 \n",
       "\n",
       "TIMEP = TP30:\n",
       " contrast     estimate     SE   df t.ratio p.value\n",
       " Verum - Sham  -0.0787 0.0394 39.8 -1.998  0.0526 \n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`simple contrasts for TIMEP`</dt>\n",
       "\t\t<dd><table class=\"dataframe\">\n",
       "<caption>A summary_emm: 6 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>contrast</th><th scope=col>GROUP</th><th scope=col>estimate</th><th scope=col>SE</th><th scope=col>df</th><th scope=col>lower.CL</th><th scope=col>upper.CL</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Bsl - TP10 </td><td>Verum</td><td>0.10262308</td><td>0.03521946</td><td>71.28469</td><td> 0.03240233</td><td>0.17284384</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Bsl - TP30 </td><td>Verum</td><td>0.12620620</td><td>0.03413419</td><td>70.41645</td><td> 0.05813477</td><td>0.19427762</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>TP10 - TP30</td><td>Verum</td><td>0.02358311</td><td>0.03740090</td><td>72.22189</td><td>-0.05097032</td><td>0.09813654</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>Bsl - TP10 </td><td>Sham </td><td>0.10262308</td><td>0.03521946</td><td>71.28469</td><td> 0.03240233</td><td>0.17284384</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>Bsl - TP30 </td><td>Sham </td><td>0.12620620</td><td>0.03413419</td><td>70.41645</td><td> 0.05813477</td><td>0.19427762</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>TP10 - TP30</td><td>Sham </td><td>0.02358311</td><td>0.03740090</td><td>72.22189</td><td>-0.05097032</td><td>0.09813654</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$`simple contrasts for GROUP`</dt>\n",
       "\t\t<dd><table class=\"dataframe\">\n",
       "<caption>A summary_emm: 3 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>contrast</th><th scope=col>TIMEP</th><th scope=col>estimate</th><th scope=col>SE</th><th scope=col>df</th><th scope=col>lower.CL</th><th scope=col>upper.CL</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Verum - Sham</td><td>Bsl </td><td>-0.07872659</td><td>0.03940385</td><td>39.78534</td><td>-0.1583781</td><td>0.0009249465</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Verum - Sham</td><td>TP10</td><td>-0.07872659</td><td>0.03940385</td><td>39.78534</td><td>-0.1583781</td><td>0.0009249465</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>Verum - Sham</td><td>TP30</td><td>-0.07872659</td><td>0.03940385</td><td>39.78534</td><td>-0.1583781</td><td>0.0009249465</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`simple contrasts for TIMEP`] A summary\\_emm: 6 × 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       "  & contrast & GROUP & estimate & SE & df & lower.CL & upper.CL\\\\\n",
       "  & <fct> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Bsl - TP10  & Verum & 0.10262308 & 0.03521946 & 71.28469 &  0.03240233 & 0.17284384\\\\\n",
       "\t2 & Bsl - TP30  & Verum & 0.12620620 & 0.03413419 & 70.41645 &  0.05813477 & 0.19427762\\\\\n",
       "\t3 & TP10 - TP30 & Verum & 0.02358311 & 0.03740090 & 72.22189 & -0.05097032 & 0.09813654\\\\\n",
       "\t4 & Bsl - TP10  & Sham  & 0.10262308 & 0.03521946 & 71.28469 &  0.03240233 & 0.17284384\\\\\n",
       "\t5 & Bsl - TP30  & Sham  & 0.12620620 & 0.03413419 & 70.41645 &  0.05813477 & 0.19427762\\\\\n",
       "\t6 & TP10 - TP30 & Sham  & 0.02358311 & 0.03740090 & 72.22189 & -0.05097032 & 0.09813654\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$`simple contrasts for GROUP`] A summary\\_emm: 3 × 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       "  & contrast & TIMEP & estimate & SE & df & lower.CL & upper.CL\\\\\n",
       "  & <fct> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Verum - Sham & Bsl  & -0.07872659 & 0.03940385 & 39.78534 & -0.1583781 & 0.0009249465\\\\\n",
       "\t2 & Verum - Sham & TP10 & -0.07872659 & 0.03940385 & 39.78534 & -0.1583781 & 0.0009249465\\\\\n",
       "\t3 & Verum - Sham & TP30 & -0.07872659 & 0.03940385 & 39.78534 & -0.1583781 & 0.0009249465\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`simple contrasts for TIMEP`\n",
       ":   \n",
       "A summary_emm: 6 × 7\n",
       "\n",
       "| <!--/--> | contrast &lt;fct&gt; | GROUP &lt;fct&gt; | estimate &lt;dbl&gt; | SE &lt;dbl&gt; | df &lt;dbl&gt; | lower.CL &lt;dbl&gt; | upper.CL &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 1 | Bsl - TP10  | Verum | 0.10262308 | 0.03521946 | 71.28469 |  0.03240233 | 0.17284384 |\n",
       "| 2 | Bsl - TP30  | Verum | 0.12620620 | 0.03413419 | 70.41645 |  0.05813477 | 0.19427762 |\n",
       "| 3 | TP10 - TP30 | Verum | 0.02358311 | 0.03740090 | 72.22189 | -0.05097032 | 0.09813654 |\n",
       "| 4 | Bsl - TP10  | Sham  | 0.10262308 | 0.03521946 | 71.28469 |  0.03240233 | 0.17284384 |\n",
       "| 5 | Bsl - TP30  | Sham  | 0.12620620 | 0.03413419 | 70.41645 |  0.05813477 | 0.19427762 |\n",
       "| 6 | TP10 - TP30 | Sham  | 0.02358311 | 0.03740090 | 72.22189 | -0.05097032 | 0.09813654 |\n",
       "\n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       ":   \n",
       "A summary_emm: 3 × 7\n",
       "\n",
       "| <!--/--> | contrast &lt;fct&gt; | TIMEP &lt;fct&gt; | estimate &lt;dbl&gt; | SE &lt;dbl&gt; | df &lt;dbl&gt; | lower.CL &lt;dbl&gt; | upper.CL &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 1 | Verum - Sham | Bsl  | -0.07872659 | 0.03940385 | 39.78534 | -0.1583781 | 0.0009249465 |\n",
       "| 2 | Verum - Sham | TP10 | -0.07872659 | 0.03940385 | 39.78534 | -0.1583781 | 0.0009249465 |\n",
       "| 3 | Verum - Sham | TP30 | -0.07872659 | 0.03940385 | 39.78534 | -0.1583781 | 0.0009249465 |\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`simple contrasts for TIMEP`\n",
       "GROUP = Verum:\n",
       " contrast    estimate     SE   df lower.CL upper.CL\n",
       " Bsl - TP10    0.1026 0.0352 71.3   0.0324   0.1728\n",
       " Bsl - TP30    0.1262 0.0341 70.4   0.0581   0.1943\n",
       " TP10 - TP30   0.0236 0.0374 72.2  -0.0510   0.0981\n",
       "\n",
       "GROUP = Sham:\n",
       " contrast    estimate     SE   df lower.CL upper.CL\n",
       " Bsl - TP10    0.1026 0.0352 71.3   0.0324   0.1728\n",
       " Bsl - TP30    0.1262 0.0341 70.4   0.0581   0.1943\n",
       " TP10 - TP30   0.0236 0.0374 72.2  -0.0510   0.0981\n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "Confidence level used: 0.95 \n",
       "\n",
       "$`simple contrasts for GROUP`\n",
       "TIMEP = Bsl:\n",
       " contrast     estimate     SE   df lower.CL upper.CL\n",
       " Verum - Sham  -0.0787 0.0394 39.8   -0.158 0.000925\n",
       "\n",
       "TIMEP = TP10:\n",
       " contrast     estimate     SE   df lower.CL upper.CL\n",
       " Verum - Sham  -0.0787 0.0394 39.8   -0.158 0.000925\n",
       "\n",
       "TIMEP = TP30:\n",
       " contrast     estimate     SE   df lower.CL upper.CL\n",
       " Verum - Sham  -0.0787 0.0394 39.8   -0.158 0.000925\n",
       "\n",
       "Degrees-of-freedom method: kenward-roger \n",
       "Confidence level used: 0.95 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 8 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>GROUP</th><th scope=col>TIMEP</th><th scope=col>N</th><th scope=col>NDR</th><th scope=col>sd</th><th scope=col>se</th><th scope=col>ci</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Verum</td><td>Bsl </td><td>29</td><td>1.0000000</td><td>0.0000000</td><td>0.00000000</td><td>0.00000000</td></tr>\n",
       "\t<tr><td>Verum</td><td>TP0 </td><td>29</td><td>0.8841769</td><td>0.2139038</td><td>0.03972093</td><td>0.08136465</td></tr>\n",
       "\t<tr><td>Verum</td><td>TP10</td><td>20</td><td>0.8394572</td><td>0.2204343</td><td>0.04929060</td><td>0.10316641</td></tr>\n",
       "\t<tr><td>Verum</td><td>TP30</td><td>23</td><td>0.8169281</td><td>0.1806023</td><td>0.03765818</td><td>0.07809829</td></tr>\n",
       "\t<tr><td>Sham </td><td>Bsl </td><td>15</td><td>1.0000000</td><td>0.0000000</td><td>0.00000000</td><td>0.00000000</td></tr>\n",
       "\t<tr><td>Sham </td><td>TP0 </td><td>15</td><td>0.9030615</td><td>0.2317670</td><td>0.05984198</td><td>0.12834827</td></tr>\n",
       "\t<tr><td>Sham </td><td>TP10</td><td>13</td><td>0.9509429</td><td>0.3052209</td><td>0.08465304</td><td>0.18444313</td></tr>\n",
       "\t<tr><td>Sham </td><td>TP30</td><td>11</td><td>0.9778468</td><td>0.2445023</td><td>0.07372022</td><td>0.16425889</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 8 × 7\n",
       "\\begin{tabular}{lllllll}\n",
       " GROUP & TIMEP & N & NDR & sd & se & ci\\\\\n",
       " <fct> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Verum & Bsl  & 29 & 1.0000000 & 0.0000000 & 0.00000000 & 0.00000000\\\\\n",
       "\t Verum & TP0  & 29 & 0.8841769 & 0.2139038 & 0.03972093 & 0.08136465\\\\\n",
       "\t Verum & TP10 & 20 & 0.8394572 & 0.2204343 & 0.04929060 & 0.10316641\\\\\n",
       "\t Verum & TP30 & 23 & 0.8169281 & 0.1806023 & 0.03765818 & 0.07809829\\\\\n",
       "\t Sham  & Bsl  & 15 & 1.0000000 & 0.0000000 & 0.00000000 & 0.00000000\\\\\n",
       "\t Sham  & TP0  & 15 & 0.9030615 & 0.2317670 & 0.05984198 & 0.12834827\\\\\n",
       "\t Sham  & TP10 & 13 & 0.9509429 & 0.3052209 & 0.08465304 & 0.18444313\\\\\n",
       "\t Sham  & TP30 & 11 & 0.9778468 & 0.2445023 & 0.07372022 & 0.16425889\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 8 × 7\n",
       "\n",
       "| GROUP &lt;fct&gt; | TIMEP &lt;fct&gt; | N &lt;dbl&gt; | NDR &lt;dbl&gt; | sd &lt;dbl&gt; | se &lt;dbl&gt; | ci &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| Verum | Bsl  | 29 | 1.0000000 | 0.0000000 | 0.00000000 | 0.00000000 |\n",
       "| Verum | TP0  | 29 | 0.8841769 | 0.2139038 | 0.03972093 | 0.08136465 |\n",
       "| Verum | TP10 | 20 | 0.8394572 | 0.2204343 | 0.04929060 | 0.10316641 |\n",
       "| Verum | TP30 | 23 | 0.8169281 | 0.1806023 | 0.03765818 | 0.07809829 |\n",
       "| Sham  | Bsl  | 15 | 1.0000000 | 0.0000000 | 0.00000000 | 0.00000000 |\n",
       "| Sham  | TP0  | 15 | 0.9030615 | 0.2317670 | 0.05984198 | 0.12834827 |\n",
       "| Sham  | TP10 | 13 | 0.9509429 | 0.3052209 | 0.08465304 | 0.18444313 |\n",
       "| Sham  | TP30 | 11 | 0.9778468 | 0.2445023 | 0.07372022 | 0.16425889 |\n",
       "\n"
      ],
      "text/plain": [
       "  GROUP TIMEP N  NDR       sd        se         ci        \n",
       "1 Verum Bsl   29 1.0000000 0.0000000 0.00000000 0.00000000\n",
       "2 Verum TP0   29 0.8841769 0.2139038 0.03972093 0.08136465\n",
       "3 Verum TP10  20 0.8394572 0.2204343 0.04929060 0.10316641\n",
       "4 Verum TP30  23 0.8169281 0.1806023 0.03765818 0.07809829\n",
       "5 Sham  Bsl   15 1.0000000 0.0000000 0.00000000 0.00000000\n",
       "6 Sham  TP0   15 0.9030615 0.2317670 0.05984198 0.12834827\n",
       "7 Sham  TP10  13 0.9509429 0.3052209 0.08465304 0.18444313\n",
       "8 Sham  TP30  11 0.9778468 0.2445023 0.07372022 0.16425889"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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HXUI5B0BGggcadUWZ5aPvOef2p48O3233zQ5fCE/skysBpLAsuDK+5uV/vDrvaH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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML. t-tests use Satterthwaite's method [\n",
       "lmerModLmerTest]\n",
       "Formula: NDR ~ 1 + GROUP + (1 | SUBJECT)\n",
       "   Data: ndr\n",
       "\n",
       "REML criterion at convergence: -62.8\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.6180 -0.5741  0.2021  0.6132  2.7832 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " SUBJECT  (Intercept) 0.00934  0.09665 \n",
       " Residual             0.03002  0.17326 \n",
       "Number of obs: 155, groups:  SUBJECT, 44\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error       df t value Pr(>|t|)    \n",
       "(Intercept)  0.89636    0.02504 43.21403  35.794   <2e-16 ***\n",
       "GROUPSham    0.05339    0.04256 42.41621   1.254    0.217    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "          (Intr)\n",
       "GROUPSham -0.588"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing profile confidence intervals ...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 4 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>.sig01</th><td> 0.05034832</td><td>0.1352448</td></tr>\n",
       "\t<tr><th scope=row>.sigma</th><td> 0.15284225</td><td>0.1985137</td></tr>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 0.84744606</td><td>0.9455189</td></tr>\n",
       "\t<tr><th scope=row>GROUPSham</th><td>-0.03043357</td><td>0.1364436</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t.sig01 &  0.05034832 & 0.1352448\\\\\n",
       "\t.sigma &  0.15284225 & 0.1985137\\\\\n",
       "\t(Intercept) &  0.84744606 & 0.9455189\\\\\n",
       "\tGROUPSham & -0.03043357 & 0.1364436\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % |\n",
       "|---|---|---|\n",
       "| .sig01 |  0.05034832 | 0.1352448 |\n",
       "| .sigma |  0.15284225 | 0.1985137 |\n",
       "| (Intercept) |  0.84744606 | 0.9455189 |\n",
       "| GROUPSham | -0.03043357 | 0.1364436 |\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %       97.5 %   \n",
       ".sig01       0.05034832 0.1352448\n",
       ".sigma       0.15284225 0.1985137\n",
       "(Intercept)  0.84744606 0.9455189\n",
       "GROUPSham   -0.03043357 0.1364436"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 1 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>NumDF</th><th scope=col>DenDF</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>GROUP</th><td>0.04723591</td><td>0.04723591</td><td>1</td><td>42.41621</td><td>1.573578</td><td>0.2165569</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 1 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Sum Sq & Mean Sq & NumDF & DenDF & F value & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tGROUP & 0.04723591 & 0.04723591 & 1 & 42.41621 & 1.573578 & 0.2165569\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 1 × 6\n",
       "\n",
       "| <!--/--> | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | NumDF &lt;int&gt; | DenDF &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| GROUP | 0.04723591 | 0.04723591 | 1 | 42.41621 | 1.573578 | 0.2165569 |\n",
       "\n"
      ],
      "text/plain": [
       "      Sum Sq     Mean Sq    NumDF DenDF    F value  Pr(>F)   \n",
       "GROUP 0.04723591 0.04723591 1     42.41621 1.573578 0.2165569"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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SiH8SerxTb9qtiOPHLZCWpIxMy8rVtu98X1l8kd7jC7/0XPCX/6x9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\nOR0AAADGGRMF6JdeeunQoUMiUlBQs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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mQN+D+k5+Ok5ZNrobeDPyBJXXldCBETouvjQUzqHuAVkyW583RGZSkkSUIIwzBD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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Grouping 2 Verum groups in a single one \n",
    "\n",
    "# install.packages('Rmisc')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "library(Rmisc)\n",
    "library(lmerTest) \n",
    "library(emmeans)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "levels(ndr$GROUP)\n",
    "levels(ndr$GROUP) <- c(\"Verum\", \"Verum\", \"Sham\")\n",
    "levels(ndr$GROUP)\n",
    "\n",
    "## SIMPLE PLOTS\n",
    "options(repr.plot.width = 8, repr.plot.height = 6)\n",
    "ggline(ndr, x = \"TIMEP\", y = \"NDR\", add = \"mean_sd\", color = \"GROUP\", palette = \"jco\", size=2, point.size=2,\n",
    "      legend=\"top\", legend.title=\"GROUP\", font.legend=c(24, \"bold\"))+ ylim(0.6, 1.2) +\n",
    "theme(axis.title.x=element_text(size=24, face=\"bold\"), axis.title.y=element_text(size=24, face=\"bold\"), \n",
    "      axis.line=element_line(size=2), axis.text=element_text(size=24, face=\"bold\"))+\n",
    "stat_compare_means(aes(group= GROUP), size=7, label = \"p.signif\")\n",
    "\n",
    "## IDENTIFY OUTLIERS FOR EACH GROUP OR ACROSS TIMEP\n",
    "# betweenstats because it was a parallel design n=45\n",
    "# options(repr.plot.width = 14, repr.plot.height = 21)\n",
    "# grouped_ggbetweenstats(data=ndr, x=TIMEP, y=NDR, grouping.var=GROUP, type = \"np\", pairwise.comparisons=FALSE,\n",
    "#                       outlier.tagging=TRUE, outlier.label=X, outlier.color='red', effsize.type=\"eta\", outlier.coef=1,\n",
    "#                        # arguments relevant for ggstatsplot::combine_plots\n",
    "#                       annotation.args = list(title = \"NDR over TIMEP and GROUPs\"),\n",
    "#                       plotgrid.args = list(ncol = 1))\n",
    "# ## Tukey=1.5\n",
    "# ndr$NDR[48] <- NA\n",
    "# ndr$NDR[45] <- NA\n",
    "# ndr$NDR[101] <- NA\n",
    "# ndr$NDR[68] <- NA\n",
    "# ndr$NDR[56] <- NA\n",
    "# ## Tukey=1.2\n",
    "# ndr$NDR[61] <- NA\n",
    "# ndr$NDR[68] <- NA\n",
    "# ndr$NDR[78] <- NA\n",
    "# ## Tukey=1\n",
    "# ndr$NDR[139] <- NA\n",
    "# ndr$NDR[113] <- NA\n",
    "# options(repr.plot.width = 8, repr.plot.height = 6)\n",
    "# ggline(ndr, x = \"TIMEP\", y = \"NDR\", add = \"mean_sd\", color = \"GROUP\", palette = \"jco\", size=2, point.size=2,\n",
    "#       legend=\"top\", legend.title=\"GROUP\", font.legend=c(24, \"bold\"))+ ylim(0.6, 1.2) +\n",
    "# theme(axis.title.x=element_text(size=24, face=\"bold\"), axis.title.y=element_text(size=24, face=\"bold\"), \n",
    "#       axis.line=element_line(size=2), axis.text=element_text(size=24, face=\"bold\"))+\n",
    "# stat_compare_means(aes(group= GROUP), size=7, label = \"p.signif\")\n",
    "\n",
    "# MODEL GROUP DIFFERENCES ACROSS TIMEP\n",
    "# ndr$TIMEP <- relevel(ndr$TIMEP,\"TP0\")   # changed the intercept to TIMEP:TP0\n",
    "mlm5 <- lmer(NDR ~ 1 + TIMEP+GROUP*WPLIG + (1|SUBJECT), data=ndr, REML=TRUE)\n",
    "summary(mlm5)\n",
    "confint(mlm5)\n",
    "anova(mlm5, type=2)\n",
    "emm5 = emmeans(mlm5, ~ TIMEP+GROUP, ddf=\"Kenward-Roger\")\n",
    "pairs(emm5, simple='each', adjust=\"none\")\n",
    "confint(pairs(emm5, simple='each', adjust=\"none\"))\n",
    "\n",
    "# Calculate SD, SE, CI from the model\n",
    "ndr_int <- summarySE(ndr, measurevar=\"NDR\", groupvars=c(\"GROUP\",\"TIMEP\"))\n",
    "ndr_int\n",
    "\n",
    "# Use GROUP as a factor and TIMEP rather as numeric\n",
    "ndr_int$GROUP <- factor(ndr_int$GROUP)\n",
    "ndr_int$TIMEP <- c(ndr_int$TIMEP)\n",
    "\n",
    "pd <- position_dodge(0.15) # move them .05 to the left and right\n",
    "ggplot(ndr_int, aes(x=TIMEP, y=NDR, colour=GROUP)) + \n",
    "    geom_errorbar(aes(ymin=NDR-sd, ymax=NDR+sd), width=.1, position=pd) +\n",
    "    geom_line(position=pd)\n",
    "#     scale_x_discrete(breaks=c(\"1\",\"2\",\"3\",\"4\"),\n",
    "#                      labels=c(\"Bsl\",\"TP0\",\"TP10\",\"TP30\"))\n",
    "\n",
    "mlm6 <- lmer(NDR ~ 1 + GROUP + (1|SUBJECT), data=ndr, REML=TRUE)\n",
    "summary(mlm6)\n",
    "confint(mlm6)\n",
    "anova(mlm6, type=2)\n",
    "\n",
    "# Fit first degree polynomial equation\n",
    "fit  <- lm(NDR ~ GROUP, data=ndr)\n",
    "ggplot(data=ndr_int, aes(x=TIMEP, y=NDR, colour=GROUP))+\n",
    "        geom_point() +\n",
    "        geom_smooth(method=\"lm\")\n",
    "\n",
    "# Fit high order degree polynomial equation\n",
    "# fit2  <- lm(NDR ~ poly(GROUP,2), data=ndr)\n",
    "# ggplot(data=ndr_int, aes(x=TIMEP, y=NDR, colour=GROUP))+\n",
    "#         geom_point() +\n",
    "#         geom_smooth(method=\"lm\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AQCGrnpB4cHf3B4UOlRAACAHGRUegCA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tGRkZUTujNSlpsKdiZv5Ge3u7Xq8fPXq0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\nnpgzZ47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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Correlation graphs Verum vs. Sham\n",
    "\n",
    "# install.packages('effects')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "plot_model(mlm5, type = \"eff\", show.data = T, terms = c('WPLIG','GROUP'))#, axis.lim= list(c(0.5,1.5), c(0.5, 1.3)))#,'TIMEP'))\n",
    "# ggsave('WPLIA_2Groups.png', plot = last_plot(), scale = 1, width = 20, height = 10, units = c('cm'), dpi = 300, limitsize = TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: lattice\n",
      "\n",
      "Loading required package: plyr\n",
      "\n",
      "Loading required package: lme4\n",
      "\n",
      "Loading required package: Matrix\n",
      "\n",
      "\n",
      "Attaching package: ‘lmerTest’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:lme4’:\n",
      "\n",
      "    lmer\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    step\n",
      "\n",
      "\n",
      "Registered S3 methods overwritten by 'car':\n",
      "  method                          from\n",
      "  influence.merMod                lme4\n",
      "  cooks.distance.influence.merMod lme4\n",
      "  dfbeta.influence.merMod         lme4\n",
      "  dfbetas.influence.merMod        lme4\n",
      "\n",
      "\n",
      "Attaching package: ‘ggpubr’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:plyr’:\n",
      "\n",
      "    mutate\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'aV1-gV5'</li><li>'gV1-aV5'</li><li>'Sham'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'aV1-gV5'\n",
       "\\item 'gV1-aV5'\n",
       "\\item 'Sham'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'aV1-gV5'\n",
       "2. 'gV1-aV5'\n",
       "3. 'Sham'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"aV1-gV5\" \"gV1-aV5\" \"Sham\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'Bsl'</li><li>'TP0'</li><li>'TP10'</li><li>'TP30'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Bsl'\n",
       "\\item 'TP0'\n",
       "\\item 'TP10'\n",
       "\\item 'TP30'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Bsl'\n",
       "2. 'TP0'\n",
       "3. 'TP10'\n",
       "4. 'TP30'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Bsl\"  \"TP0\"  \"TP10\" \"TP30\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>72</li><li>23</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 72\n",
       "\\item 23\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 72\n",
       "2. 23\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 72 23"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Grouping 2 Verum groups in a single one \n",
    "\n",
    "# install.packages('Rmisc')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "library(Rmisc)\n",
    "library(lmerTest) \n",
    "library(emmeans)\n",
    "library(ggpubr)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "ndr <- ndr[!(ndr$TIMEP==\"TP0\"),] # drop all data from TP0\n",
    "ndr <- ndr[!(ndr$GROUP==\"Sham\"),] # drop all data from Sham\n",
    "# levels(ndr$GROUP) <- c(\"Verum\", \"Verum\", \"Sham\")\n",
    "levels(ndr$GROUP)\n",
    "levels(ndr$TIMEP)\n",
    "dim(ndr)\n",
    "\n",
    "## SIMPLE PLOTS\n",
    "options(repr.plot.width = 8, repr.plot.height = 6)\n",
    "ggline(ndr, x = \"TIMEP\", y = \"V1pV5a\", add = \"mean_sd\", color = \"GROUP\", palette = \"jco\", size=2, point.size=2,\n",
    "      legend=\"top\", legend.title=\"GROUP\", font.legend=c(24, \"bold\"))+ #ylim(-2, 7) + \n",
    "theme(axis.title.x=element_text(size=24, face=\"bold\"), axis.title.y=element_text(size=24, face=\"bold\"), \n",
    "      axis.line=element_line(size=2), axis.text=element_text(size=24, face=\"bold\"))#+\n",
    "# stat_compare_means(aes(group= GROUP), size=7, label = \"p.signif\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>155</li><li>23</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 155\n",
       "\\item 23\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 155\n",
       "2. 23\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 155  23"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'aV1-gV5'</li><li>'gV1-aV5'</li><li>'Sham'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'aV1-gV5'\n",
       "\\item 'gV1-aV5'\n",
       "\\item 'Sham'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'aV1-gV5'\n",
       "2. 'gV1-aV5'\n",
       "3. 'Sham'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"aV1-gV5\" \"gV1-aV5\" \"Sham\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'Bsl'</li><li>'TP0'</li><li>'TP10'</li><li>'TP30'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Bsl'\n",
       "\\item 'TP0'\n",
       "\\item 'TP10'\n",
       "\\item 'TP30'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Bsl'\n",
       "2. 'TP0'\n",
       "3. 'TP10'\n",
       "4. 'TP30'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Bsl\"  \"TP0\"  \"TP10\" \"TP30\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
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AAAADhXC57/Ur1eteShBeuZhdqvmv3HuQohdmrqvmIxGhZRMg2Nca4AACEEgR0A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\nCkV2ZN/Gs8/ta2MHAHACBHbAEXurP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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
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JUNaVmVyujWDACYDAR2AAAAACAW4l5XeW2luhcTutOen6N2TgizUmlIK8vmmlI2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\n6XmOUv3t57rKC5Jk+DNUNe0G02hJubTxnC0b0pou1dhWjNlmuko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EKL+TiaX9z//LwsKCbdvjXgiWhEl63PM6ruoslc6p4znHtlY17aBp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\nQv8YwoHxeDwYDDY3N520LIvJZDIaj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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Correlation graphs: EEG vs. NDR\n",
    "\n",
    "# install.packages('Rmisc')\n",
    "library(sjPlot)\n",
    "library(ggplot2)\n",
    "library(Rmisc)\n",
    "library(lmerTest) \n",
    "library(emmeans)\n",
    "library(ggpubr)\n",
    "\n",
    "set_theme(\n",
    "  axis.title.size = 2,\n",
    "  axis.textsize = 1.5,\n",
    "  legend.size = 2,\n",
    "  title.size = 2, \n",
    "  base = theme_bw()\n",
    ")\n",
    "\n",
    "ndr <- read.table('II_Mixed_mod_Prepro.txt',header=TRUE,sep='\\t')\n",
    "# head(ndr[5:15])\n",
    "dim(ndr)\n",
    "levels(ndr$GROUP)\n",
    "levels(ndr$TIMEP)\n",
    "\n",
    "ndr <- ndr[!(ndr$TIMEP==\"TP0\"),] # drop all data from TP0\n",
    "ndr <- ndr[!(ndr$GROUP==\"Sham\"),] # drop all data from Sham\n",
    "\n",
    "options(repr.plot.width = 14, repr.plot.height = 5)\n",
    "b <- ggplot(ndr, aes(x = V1aV5p, y = NDR))\n",
    "b + geom_point(aes(color = GROUP, shape = GROUP)) +\n",
    "  geom_smooth(aes(color = GROUP), method = lm, se = FALSE, fullrange = TRUE)+\n",
    "  ggpubr::stat_cor(aes(color = GROUP), label.x = -3, size = 2)+\n",
    "  theme(axis.title.x=element_text(size=4, face=\"bold\"), axis.title.y=element_text(size=4, face=\"bold\"), \n",
    "      axis.line=element_line(size=0), axis.text=element_text(size=14, face=\"bold\"),\n",
    "      legend.text = element_text(size=4, face=\"bold\"), legend.title = element_text(size=4, face=\"bold\"))\n",
    "# ggsave('V1aV5p.png', plot = last_plot(), scale = 1, width = 15, height = 5, units = c('cm'), dpi = 300, limitsize = TRUE)\n",
    "\n",
    "\n",
    "c <- ggplot(ndr, aes(x = WPLIA, y = NDR))\n",
    "c + geom_point(aes(color = GROUP, shape = GROUP)) +\n",
    "  geom_smooth(aes(color = GROUP), method = lm, se = FALSE, fullrange = TRUE)+\n",
    "  ggpubr::stat_cor(aes(color = GROUP), label.x = 0.5, size = 2)+\n",
    "  theme(axis.title.x=element_text(size=4, face=\"bold\"), axis.title.y=element_text(size=4, face=\"bold\"), \n",
    "      axis.line=element_line(size=0), axis.text=element_text(size=14, face=\"bold\"),\n",
    "      legend.text = element_text(size=4, face=\"bold\"), legend.title = element_text(size=4, face=\"bold\"))\n",
    "# ggsave('WPLIA.png', plot = last_plot(), scale = 1, width = 15, height = 5, units = c('cm'), dpi = 300, limitsize = TRUE)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### simrOptions(progress=TRUE) #Avoid showing progress bars\n",
    "\n",
    "### Power = Pr(Reject H0 | H1 is TRUE) --> fcompare(H1) \n",
    "sim_GROUP <- powerSim(rint, nsim=20, test = fcompare(NDR~TIMEP))\n",
    "sim_GROUP\n",
    "# sim_TIMEP <- powerSim(rint, nsim=20, test = fcompare(NDR~GROUP))\n",
    "# sim_TIMEP\n",
    "# sim_TG <- powerSim(rint, nsim=20, test = fcompare(NDR~TIMEP*GROUP))\n",
    "# sim_TG\n",
    "\n",
    "# Extend the number of participants per group\n",
    "model_ext_subj <- extend(rint, along=\"SUBJECT\", n=60)\n",
    "model_ext_subj\n",
    "\n",
    "# ReTest Power with the new number of subjects\n",
    "sim_treat_subj <- powerSim(model_ext_subj, nsim=20, test=fcompare(NDR~TIMEP), progress=FALSE)\n",
    "sim_treat_subj\n",
    "\n",
    "# Plot number of subjects against Stat.Power\n",
    "p_curve_treat <- powerCurve(model_ext_subj, test=fcompare(NDR~TIMEP), along='SUBJECT',\n",
    "                            breaks=c(5,10,15,20,25,30, 40, 50, 60), progress=FALSE)\n",
    "plot(p_curve_treat)\n",
    "\n",
    "# # Change the effect size\n",
    "# model_large <- rint\n",
    "# fixef(model_large)#['TIMEP'] <- 2\n",
    "\n",
    "# sim_treat_large <- powerSim(model_large, nsim=100, test = fcompare(y~time))\n",
    "# sim_treat_large"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
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   "file_extension": ".r",
   "mimetype": "text/x-r-source",
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   "pygments_lexer": "r",
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