diff --git a/NEWS.md b/NEWS.md
index db02f1a..22e6970 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,3 +1,10 @@
+# vinereg 0.10.0
+
+NEW FEATURE
+
+ * New function `pdf()` to compute the conditional log-likelihood.
+
+
# vinereg 0.9.2
BUG FIX
diff --git a/docs/404.html b/docs/404.html
index 174e89a..0c7e488 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -32,7 +32,7 @@
vinereg
- 0.9.1
+ 0.10.0
diff --git a/docs/LICENSE-text.html b/docs/LICENSE-text.html
index 66722ae..12bec01 100644
--- a/docs/LICENSE-text.html
+++ b/docs/LICENSE-text.html
@@ -17,7 +17,7 @@
vinereg
- 0.9.1
+ 0.10.0
diff --git a/docs/articles/abalone-example.html b/docs/articles/abalone-example.html
index 06c864b..6fd7db6 100644
--- a/docs/articles/abalone-example.html
+++ b/docs/articles/abalone-example.html
@@ -33,7 +33,7 @@
vinereg
- 0.9.0
+ 0.10.0
@@ -100,51 +100,51 @@ September 2017
D-vine copula based quantile regression, Computational
Statistics and Data Analysis, 110, 1-18. Please, feel free to address
questions to daniel.kraus@tum.de.
-
-
Load required packages
-
+
-
Data analysis
-
+
We consider the data set abalone from the UCI Machine
Learning Repository (https://archive.ics.uci.edu/ml/datasets/abalone) and
focus on the female sub-population. In a first application we only
consider continuous variables and fit models to predict the quantiles of
weight (whole) given the predictors length,
diameter, and height.
-
-
Load and clean data
-
+
+
Load and clean data
+
-data(abalone, package = "AppliedPredictiveModeling")
-colnames(abalone) <- c(
- "sex", "length", "diameter", "height", "whole",
- "shucked", "viscera", "shell", "rings"
-)
-abalone_f <- abalone %>%
- dplyr::filter(sex == "F") %>% # select female abalones
- dplyr::select(-sex) %>% # remove id and sex variables
- dplyr::filter(height < max(height)) # remove height outlier
+
data(abalone, package = "AppliedPredictiveModeling")
+colnames(abalone) <- c(
+ "sex", "length", "diameter", "height", "whole",
+ "shucked", "viscera", "shell", "rings"
+)
+abalone_f <- abalone %>%
+ dplyr::filter(sex == "F") %>% # select female abalones
+ dplyr::select(-sex) %>% # remove id and sex variables
+ dplyr::filter(height < max(height)) # remove height outlier
-pairs(abalone_f, pch = ".")
+
pairs(abalone_f, pch = ".")
-
D-vine regression models
-
-
Parametric D-vine quantile regression
+D-vine regression models
+
+
Parametric D-vine quantile regression
+
We consider the female subset and fit a parametric regression D-vine
for the response weight given the covariates len, diameter and height
(ignoring the discreteness of some of the variables). The D-vine based
@@ -161,135 +161,135 @@
Parametric D-vine quantile regres
type for the conditional log-likelihood criterion for variable
selection.
-fit_vine_par <- vinereg(
- whole ~ length + diameter + height,
- data = abalone_f,
- family_set = c("onepar", "t"),
- selcrit = "aic"
-)
fit_vine_par <- vinereg(
+ whole ~ length + diameter + height,
+ data = abalone_f,
+ family_set = c("onepar", "t"),
+ selcrit = "aic"
+)
The result has a field order that shows the selected
covariates and their ranking order in the D-vine.
-
## [1] "length" "height" "diameter"
+
fit_vine_par$order
+
## [1] "length" "height" "diameter"
The field vine contains the fitted D-vine, where the
first variable corresponds to the response. The object is of class
"vinecop_dist" so we can use rvineocpulib’s
functionality to summarize the model
-
## # A data.frame: 6 x 11
-## tree edge conditioned conditioning var_types family rotation parameters df
-## 1 1 1, 2 c,c gumbel 180 5.2 1
-## 1 2 2, 4 c,c gumbel 180 2.4 1
-## 1 3 4, 3 c,c gumbel 180 2.4 1
-## 2 1 1, 4 2 c,c t 0 0.45, 20.20 2
-## 2 2 2, 3 4 c,c t 0 0.91, 4.68 2
-## 3 1 1, 3 4, 2 c,c t 0 0.31, 7.39 2
-## tau loglik
-## 0.81 1629
-## 0.58 672
-## 0.59 709
-## 0.30 147
-## 0.73 1193
-## 0.20 72
+
summary(fit_vine_par$vine)## # A data.frame: 6 x 11
+## tree edge conditioned conditioning var_types family rotation parameters df
+## 1 1 1, 2 c,c gumbel 180 5.2 1
+## 1 2 2, 4 c,c gumbel 180 2.4 1
+## 1 3 4, 3 c,c gumbel 180 2.4 1
+## 2 1 1, 4 2 c,c t 0 0.45, 20.20 2
+## 2 2 2, 3 4 c,c t 0 0.91, 4.68 2
+## 3 1 1, 3 4, 2 c,c t 0 0.31, 7.39 2
+## tau loglik
+## 0.81 1629
+## 0.58 672
+## 0.59 709
+## 0.30 147
+## 0.73 1193
+## 0.20 72
We can also plot the contours of the fitted pair-copulas.
+contour(fit_vine_par$vine)
-
-
Estimation of corresponding conditional quantiles
-
+
+
Estimation of corresponding conditional quantiles
+
In order to visualize the predicted influence of the covariates, we
plot the estimated quantiles arising from the D-vine model at levels
0.1, 0.5 and 0.9 against each of the covariates.
-# quantile levels
-alpha_vec <- c(0.1, 0.5, 0.9)
+
# quantile levels
+alpha_vec <- c(0.1, 0.5, 0.9) We call the fitted() function on
fit_vine_par to extract the fitted values for multiple
quantile levels. This is equivalent to predicting the quantile at the
training data. The latter function is more useful for out-of-sample
predictions.
-pred_vine_par <- fitted(fit_vine_par, alpha = alpha_vec)
-# equivalent to:
-# predict(fit_vine_par, newdata = abalone.f, alpha = alpha_vec)
-head(pred_vine_par)
-
## 0.1 0.5 0.9
-## 1 0.6719522 0.7666997 0.8715491
-## 2 0.6969903 0.7903960 0.9012124
-## 3 0.6794323 0.7842671 0.8916937
-## 4 0.7755592 0.8800229 0.9974089
-## 5 0.5952851 0.6997763 0.8272583
-## 6 0.6757838 0.7729635 0.8858529
+
pred_vine_par <- fitted(fit_vine_par, alpha = alpha_vec)
+# equivalent to:
+# predict(fit_vine_par, newdata = abalone.f, alpha = alpha_vec)
+head(pred_vine_par)## 0.1 0.5 0.9
+## 1 0.6719522 0.7666997 0.8715491
+## 2 0.6969903 0.7903960 0.9012124
+## 3 0.6794323 0.7842671 0.8916937
+## 4 0.7755592 0.8800229 0.9974089
+## 5 0.5952851 0.6997763 0.8272583
+## 6 0.6757838 0.7729635 0.8858529
To examine the effect of the individual variables, we will plot the
predicted quantiles against each of the variables. To visualize the
relationship more clearly, we add a smoothed line for each quantile
level. This gives an estimate of the expected effect of a variable
(taking expectation with respect to all other variables).
-## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
+plot_effects(fit_vine_par)
+## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
The fitted quantile curves suggest a non-linear effect of all three
variables.
-
-
Comparison to the benchmark model: linear quantile regression
-
+
+
Comparison to the benchmark model: linear quantile regression
+
This can be compared to linear quantile regression:
-pred_lqr <- pred_vine_par
-for (a in seq_along(alpha_vec)) {
- my.rq <- quantreg::rq(
- whole ~ length + diameter + height,
- tau = alpha_vec[a],
- data = abalone_f
- )
- pred_lqr[, a] <- quantreg::predict.rq(my.rq)
-}
-
-plot_marginal_effects <- function(covs, preds) {
- cbind(covs, preds) %>%
- tidyr::gather(alpha, prediction, -seq_len(NCOL(covs))) %>%
- dplyr::mutate(prediction = as.numeric(prediction)) %>%
- tidyr::gather(variable, value, -(alpha:prediction)) %>%
- ggplot(aes(value, prediction, color = alpha)) +
- geom_point(alpha = 0.15) +
- geom_smooth(method = "gam", formula = y ~ s(x, bs = "cs"), se = FALSE) +
- facet_wrap(~ variable, scale = "free_x") +
- ylab(quote(q(y* "|" * x[1] * ",...," * x[p]))) +
- xlab(quote(x[k])) +
- theme(legend.position = "bottom")
-}
-plot_marginal_effects(abalone_f[, 1:3], pred_lqr)
+
pred_lqr <- pred_vine_par
+for (a in seq_along(alpha_vec)) {
+ my.rq <- quantreg::rq(
+ whole ~ length + diameter + height,
+ tau = alpha_vec[a],
+ data = abalone_f
+ )
+ pred_lqr[, a] <- quantreg::predict.rq(my.rq)
+}
+
+plot_marginal_effects <- function(covs, preds) {
+ cbind(covs, preds) %>%
+ tidyr::gather(alpha, prediction, -seq_len(NCOL(covs))) %>%
+ dplyr::mutate(prediction = as.numeric(prediction)) %>%
+ tidyr::gather(variable, value, -(alpha:prediction)) %>%
+ ggplot(aes(value, prediction, color = alpha)) +
+ geom_point(alpha = 0.15) +
+ geom_smooth(method = "gam", formula = y ~ s(x, bs = "cs"), se = FALSE) +
+ facet_wrap(~ variable, scale = "free_x") +
+ ylab(quote(q(y* "|" * x[1] * ",...," * x[p]))) +
+ xlab(quote(x[k])) +
+ theme(legend.position = "bottom")
+}
+plot_marginal_effects(abalone_f[, 1:3], pred_lqr)
-
Nonparametric D-vine quantile regression
-
+
+
Nonparametric D-vine quantile regression
+
We also want to check whether these results change, when we estimate
the pair-copulas nonparametrically.
-fit_vine_np <- vinereg(
- whole ~ length + diameter + height,
- data = abalone_f,
- family_set = "nonpar",
- selcrit = "aic"
-)
-fit_vine_np
-
## D-vine regression model: whole | length, height, diameter
-## nobs = 1306, edf = 95.59, cll = 1208.61, caic = -2226.04, cbic = -1731.39
+
fit_vine_np <- vinereg(
+ whole ~ length + diameter + height,
+ data = abalone_f,
+ family_set = "nonpar",
+ selcrit = "aic"
+)
+fit_vine_np
+
## D-vine regression model: whole | length, height, diameter
+## nobs = 1306, edf = 94.85, cll = 1206.93, caic = -2224.16, cbic = -1733.35
+
contour(fit_vine_np$vine)
Now only the length and height variables are selected as predictors.
Let’s have a look at the marginal effects.
-plot_effects(fit_vine_np, var = c("diameter", "height", "length"))
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
+plot_effects(fit_vine_np, var = c("diameter", "height", "length"))
+## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
The effects look similar to the parametric one, but slightly more
wiggly. Note that even the diameter was not selected as a covariate,
@@ -297,29 +297,29 @@
Nonparametric D-vine quantile
additional information when height and length are already accounted
for.
-
-
Discrete D-vine quantile regression
-
+
+
Discrete D-vine quantile regression
+
To deal with discrete variables, we use the methodology of Schallhorn
et al. (2017). For estimating nonparametric pair-copulas with discrete
variable(s), jittering is used (Nagler, 2017).
We let vinereg() know that a variable is discrete by
declaring it ordered.
-abalone_f$rings <- as.ordered(abalone_f$rings)
-fit_disc <- vinereg(rings ~ ., data = abalone_f, selcrit = "aic")
-fit_disc
-
## D-vine regression model: rings | shell, shucked, whole, height, viscera, length, diameter
-## nobs = 1306, edf = 9, cll = -2782.06, caic = 5582.12, cbic = 5628.69
+
abalone_f$rings <- as.ordered(abalone_f$rings)
+fit_disc <- vinereg(rings ~ ., data = abalone_f, selcrit = "aic")
+fit_disc
+
## D-vine regression model: rings | shell, shucked, whole, height, viscera, length, diameter
+## nobs = 1306, edf = 9, cll = -2781.56, caic = 5581.12, cbic = 5627.7
-
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
+
plot_effects(fit_disc)## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
-
-
References
-
+
+
References
+
Kraus and Czado (2017), D-vine copula based quantile
regression, Computational Statistics and Data Analysis,
110, 1-18
@@ -348,8 +348,7 @@
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diff --git a/docs/articles/bike-rental.html b/docs/articles/bike-rental.html
index 055eb29..7acb590 100644
--- a/docs/articles/bike-rental.html
+++ b/docs/articles/bike-rental.html
@@ -33,7 +33,7 @@
vinereg
- 0.9.0
+ 0.10.0
November 8, 2017
Required packages
+library(vinereg)
+require(ggplot2)
+require(dplyr)
+require(purrr)
+require(scales)
+require(quantreg)
Plot function for marginal effects
-plot_marginal_effects <- function(covs, preds) {
- cbind(covs, preds) %>%
- tidyr::gather(alpha, prediction, -seq_len(NCOL(covs))) %>%
- dplyr::mutate(prediction = as.numeric(prediction)) %>%
- tidyr::gather(variable, value, -(alpha:prediction)) %>%
- dplyr::mutate(value = as.numeric(value)) %>%
- ggplot(aes(value, prediction, color = alpha)) +
- geom_point(alpha = 0.15) +
- geom_smooth(span = 0.5, se = FALSE) +
- facet_wrap(~ variable, scale = "free_x") +
- theme(legend.position = "none") +
- theme(plot.margin = unit(c(0, 0, 0, 0), "mm")) +
- xlab("")
-}
+
plot_marginal_effects <- function(covs, preds) {
+ cbind(covs, preds) %>%
+ tidyr::gather(alpha, prediction, -seq_len(NCOL(covs))) %>%
+ dplyr::mutate(prediction = as.numeric(prediction)) %>%
+ tidyr::gather(variable, value, -(alpha:prediction)) %>%
+ dplyr::mutate(value = as.numeric(value)) %>%
+ ggplot(aes(value, prediction, color = alpha)) +
+ geom_point(alpha = 0.15) +
+ geom_smooth(span = 0.5, se = FALSE) +
+ facet_wrap(~ variable, scale = "free_x") +
+ theme(legend.position = "none") +
+ theme(plot.margin = unit(c(0, 0, 0, 0), "mm")) +
+ xlab("")
+}
Data preparation
@@ -132,97 +132,97 @@ Data preparationLoad data
-## instant dteday season yr mnth holiday weekday workingday weathersit
-## 1 1 2011-01-01 1 0 1 0 6 0 2
-## 2 2 2011-01-02 1 0 1 0 0 0 2
-## 3 3 2011-01-03 1 0 1 0 1 1 1
-## 4 4 2011-01-04 1 0 1 0 2 1 1
-## 5 5 2011-01-05 1 0 1 0 3 1 1
-## 6 6 2011-01-06 1 0 1 0 4 1 1
-## temp atemp hum windspeed casual registered cnt
-## 1 0.344167 0.363625 0.805833 0.1604460 331 654 985
-## 2 0.363478 0.353739 0.696087 0.2485390 131 670 801
-## 3 0.196364 0.189405 0.437273 0.2483090 120 1229 1349
-## 4 0.200000 0.212122 0.590435 0.1602960 108 1454 1562
-## 5 0.226957 0.229270 0.436957 0.1869000 82 1518 1600
-## 6 0.204348 0.233209 0.518261 0.0895652 88 1518 1606
+bikedata <- read.csv("day.csv")
+bikedata[, 2] <- as.Date(bikedata[, 2])
+head(bikedata)
+## instant dteday season yr mnth holiday weekday workingday weathersit
+## 1 1 2011-01-01 1 0 1 0 6 0 2
+## 2 2 2011-01-02 1 0 1 0 0 0 2
+## 3 3 2011-01-03 1 0 1 0 1 1 1
+## 4 4 2011-01-04 1 0 1 0 2 1 1
+## 5 5 2011-01-05 1 0 1 0 3 1 1
+## 6 6 2011-01-06 1 0 1 0 4 1 1
+## temp atemp hum windspeed casual registered cnt
+## 1 0.344167 0.363625 0.805833 0.1604460 331 654 985
+## 2 0.363478 0.353739 0.696087 0.2485390 131 670 801
+## 3 0.196364 0.189405 0.437273 0.2483090 120 1229 1349
+## 4 0.200000 0.212122 0.590435 0.1602960 108 1454 1562
+## 5 0.226957 0.229270 0.436957 0.1869000 82 1518 1600
+## 6 0.204348 0.233209 0.518261 0.0895652 88 1518 1606
Rename variables
-bikedata <- bikedata %>%
- rename(
- temperature = atemp,
- month = mnth,
- weathersituation = weathersit,
- humidity = hum,
- count = cnt
- )
+
bikedata <- bikedata %>%
+ rename(
+ temperature = atemp,
+ month = mnth,
+ weathersituation = weathersit,
+ humidity = hum,
+ count = cnt
+ )
Un-normalize variables
See variable description on UCI web page.
-bikedata <- bikedata %>%
- mutate(
- temperature = 66 * temperature + 16,
- windspeed = 67 * windspeed,
- humidity = 100 * humidity
- )
+
bikedata <- bikedata %>%
+ mutate(
+ temperature = 66 * temperature + 16,
+ windspeed = 67 * windspeed,
+ humidity = 100 * humidity
+ )
Drop useless variables
-bikedata <- bikedata %>%
- select(-instant, -dteday, -yr) %>% # time indices
- select(-casual, -registered) %>% # casual + registered = count
- select(-holiday) %>% # we use 'workingday' instead
- select(-temp) # we use 'temperature' (feeling temperature)
+
bikedata <- bikedata %>%
+ select(-instant, -dteday, -yr) %>% # time indices
+ select(-casual, -registered) %>% # casual + registered = count
+ select(-holiday) %>% # we use 'workingday' instead
+ select(-temp) # we use 'temperature' (feeling temperature)
Declare discrete variables as ordered
-disc_vars <- c("season", "month", "weekday", "workingday", "weathersituation")
-bikedata <- bikedata %>%
- mutate(weekday = ifelse(weekday == 0, 7, weekday)) %>% # sun at end of week
- purrr::modify_at(disc_vars, as.ordered)
+
disc_vars <- c("season", "month", "weekday", "workingday", "weathersituation")
+bikedata <- bikedata %>%
+ mutate(weekday = ifelse(weekday == 0, 7, weekday)) %>% # sun at end of week
+ purrr::modify_at(disc_vars, as.ordered)
@@ -232,76 +232,76 @@
D-vine regression modelFit model
-fit <- vinereg(
- count ~ .,
- data = bikedata,
- family = c("onepar", "tll"),
- selcrit = "aic"
-)
-fit
## D-vine regression model: count | temperature, humidity, windspeed, month, season, weathersituation, workingday, weekday
-## nobs = 731, edf = 55.49, cll = 410.19, caic = -709.39, cbic = -454.45
+fit <- vinereg(
+ count ~ .,
+ data = bikedata,
+ family = c("onepar", "tll"),
+ selcrit = "aic"
+)
+fit
## D-vine regression model: count | temperature, humidity, windspeed, month, season, weathersituation, weekday, workingday
+## nobs = 731, edf = 72.13, cll = 435.3, caic = -726.34, cbic = -394.96
-## var edf cll caic cbic p_value
-## 1 count 9.59683 -198.076002 415.345665 459.437472 NA
-## 2 temperature 21.96569 415.796680 -787.661982 -686.742527 1.081331e-161
-## 3 humidity 17.92777 118.896648 -201.937762 -119.570188 2.228987e-40
-## 4 windspeed 1.00000 22.818931 -43.637862 -39.043448 1.422649e-11
-## 5 month 1.00000 13.494037 -24.988073 -20.393660 2.047147e-07
-## 6 season 1.00000 11.793281 -21.586562 -16.992149 1.194186e-06
-## 7 weathersituation 1.00000 11.308234 -20.616468 -16.022054 1.977821e-06
-## 8 workingday 1.00000 10.001404 -18.002808 -13.408395 7.732851e-06
-## 9 weekday 1.00000 4.152908 -6.305817 -1.711403 3.951831e-03
+summary(fit)
+## var edf cll caic cbic p_value
+## 1 count 9.59683 -198.076002 415.34567 459.43747 NA
+## 2 temperature 21.98142 415.787940 -787.61304 -686.62130 1.122645e-161
+## 3 humidity 17.93921 118.956008 -202.03360 -119.61346 2.141039e-40
+## 4 windspeed 1.00000 22.861975 -43.72395 -39.12954 1.361480e-11
+## 5 month 1.00000 13.322233 -24.64447 -20.05005 2.445501e-07
+## 6 season 1.00000 12.044517 -22.08903 -17.49462 9.198266e-07
+## 7 weathersituation 1.00000 13.248269 -24.49654 -19.90212 2.640109e-07
+## 8 weekday 17.60987 30.157881 -25.09603 55.81098 1.406307e-06
+## 9 workingday 1.00000 6.996617 -11.99323 -7.39882 1.834697e-04
In-sample predictions
-alpha_vec <- c(0.1, 0.5, 0.9)
-pred <- fitted(fit, alpha_vec)
+
alpha_vec <- c(0.1, 0.5, 0.9)
+pred <- fitted(fit, alpha_vec)
Marginal effects
-plot_marginal_effects(
- covs = select(bikedata, temperature),
- preds = pred
-)
+
plot_marginal_effects(
+ covs = select(bikedata, temperature),
+ preds = pred
+)
-plot_marginal_effects(covs = select(bikedata, humidity), preds = pred) +
- xlim(c(25, 100))
plot_marginal_effects(covs = select(bikedata, humidity), preds = pred) +
+ xlim(c(25, 100))
-plot_marginal_effects(covs = select(bikedata, windspeed), preds = pred)
plot_marginal_effects(covs = select(bikedata, windspeed), preds = pred)
-month_labs <- c("Jan","", "Mar", "", "May", "", "Jul", "", "Sep", "", "Nov", "")
-plot_marginal_effects(covs = select(bikedata, month), preds = pred) +
- scale_x_discrete(limits = 1:12, labels = month_labs)
month_labs <- c("Jan","", "Mar", "", "May", "", "Jul", "", "Sep", "", "Nov", "")
+plot_marginal_effects(covs = select(bikedata, month), preds = pred) +
+ scale_x_discrete(limits = 1:12, labels = month_labs)
-plot_marginal_effects(covs = select(bikedata, weathersituation),
- preds = pred) +
- scale_x_discrete(limits = 1:3,labels = c("good", "medium", "bad"))
plot_marginal_effects(covs = select(bikedata, weathersituation),
+ preds = pred) +
+ scale_x_discrete(limits = 1:3,labels = c("good", "medium", "bad"))
-weekday_labs <- c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")
-plot_marginal_effects(covs = select(bikedata, weekday), preds = pred) +
- scale_x_discrete(limits = 1:7, labels = weekday_labs)
weekday_labs <- c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")
+plot_marginal_effects(covs = select(bikedata, weekday), preds = pred) +
+ scale_x_discrete(limits = 1:7, labels = weekday_labs)
+plot_marginal_effects(covs = select(bikedata, workingday), preds = pred) +
+ scale_x_discrete(limits = 0:1, labels = c("no", "yes")) +
+ geom_smooth(method = "lm", se = FALSE) +
+ xlim(c(0, 1))
-season_labs <- c("spring", "summer", "fall", "winter")
-plot_marginal_effects(covs = select(bikedata, season), preds = pred) +
- scale_x_discrete(limits = 1:4, labels = season_labs)
season_labs <- c("spring", "summer", "fall", "winter")
+plot_marginal_effects(covs = select(bikedata, season), preds = pred) +
+ scale_x_discrete(limits = 1:4, labels = season_labs)
@@ -324,8 +324,7 @@ 
