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<!DOCTYPE html>
<html lang="en"><head>
<script src="women-in-stem_files/libs/clipboard/clipboard.min.js"></script>
<script src="women-in-stem_files/libs/quarto-html/tabby.min.js"></script>
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<link href="women-in-stem_files/libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles"><meta charset="utf-8">
<meta name="generator" content="quarto-1.1.189">
<meta name="author" content="Lydia Gibson">
<title>Practicality of Using Transformations in MLR</title>
<meta name="apple-mobile-web-app-capable" content="yes">
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<div class="reveal">
<div class="slides">
<section id="title-slide" class="center">
<h1 class="title">Practicality of Using Transformations in MLR</h1>
<p class="author">Lydia Gibson</p>
</section>
<section id="introduction" class="title-slide slide level1 center">
<h1>Introduction</h1>
<div class="cell">
</div>
<ul>
<li>In previous research, I’ve used multiple linear regression <strong>(MLR)</strong> to explore the relationship between median salary of STEM majors and gender demographics.</li>
<li>The final reduced model used the inverse transformation of the response variable, due to the skewness of it’s distribution, to improve the model fit.</li>
<li>While transforming response variables can lead to better fitting models, these models are not easy to explain.</li>
</ul>
</section>
<section id="outline" class="title-slide slide level1 center">
<h1>Outline</h1>
<p>Problem</p>
<p>Data Source</p>
<p>Methods</p>
<p>Results</p>
<p>Conclusion</p>
<p>Further Research</p>
</section>
<section id="problem" class="title-slide slide level1 center">
<h1>Problem</h1>
<ul>
<li><p>How much prediction power is lost by <strong><em>not</em></strong> using a transformed response variable in a linear regression model?</p></li>
<li><p>Is it worth the inability to easily explain your model?</p></li>
</ul>
</section>
<section>
<section id="data-source" class="title-slide slide level1 center">
<h1>Data Source</h1>
<ul>
<li>The <a href="https://github.com/fivethirtyeight/data/blob/master/college-majors/women-stem.csv">data set</a> was obtained from the American Community Survey (ACS) 2010-2012 Public Use Microdata Series (PUMS).</li>
<li>It has 76 observations and 9 variables.</li>
</ul>
<div class="cell">
</div>
</section>
<section id="exploratory-data-analysis" class="slide level2">
<h2>Exploratory Data Analysis</h2>
<img data-src="women-in-stem_files/figure-revealjs/unnamed-chunk-4-1.png" width="960" class="r-stretch"></section></section>
<section>
<section id="method" class="title-slide slide level1 center">
<h1>Method</h1>
</section>
<section id="model-without-transformation" class="slide level2">
<h2>Model <em>Without</em> Transformation</h2>
<div class="cell">
<div class="cell-output cell-output-stdout">
<pre><code>Parameter | Coefficient | SE | 95% CI | t(71) | p
--------------------------------------------------------------------------------------------------------
(Intercept) | 36421.43 | 2597.45 | [31242.27, 41600.59] | 14.02 | < .001
Major category [Computers & Mathematics] | 6324.03 | 3915.80 | [-1483.85, 14131.90] | 1.62 | 0.111
Major category [Engineering] | 20961.33 | 3162.87 | [14654.74, 27267.92] | 6.63 | < .001
Major category [Health] | 403.57 | 3823.34 | [-7219.95, 8027.09] | 0.11 | 0.916
Major category [Physical Sciences] | 5468.57 | 4023.95 | [-2554.95, 13492.09] | 1.36 | 0.178 </code></pre>
</div>
</div>
</section>
<section id="why-a-transformation" class="slide level2">
<h2>Why a Transformation?</h2>
<img data-src="women-in-stem_files/figure-revealjs/unnamed-chunk-6-1.png" width="960" class="r-stretch"></section>
<section id="model-with-transformation" class="slide level2">
<h2>Model <em>With</em> Transformation</h2>
<div class="cell">
<div class="cell-output cell-output-stdout">
<pre><code>Parameter | Coefficient | SE | 95% CI | t(71) | p
---------------------------------------------------------------------------------------------------
(Intercept) | 2.79e-05 | 9.88e-07 | [ 0.00, 0.00] | 28.23 | < .001
Major category [Computers & Mathematics] | -4.19e-06 | 1.49e-06 | [ 0.00, 0.00] | -2.81 | 0.006
Major category [Engineering] | -9.69e-06 | 1.20e-06 | [ 0.00, 0.00] | -8.06 | < .001
Major category [Health] | -1.47e-07 | 1.45e-06 | [ 0.00, 0.00] | -0.10 | 0.920
Major category [Physical Sciences] | -3.33e-06 | 1.53e-06 | [ 0.00, 0.00] | -2.17 | 0.033 </code></pre>
</div>
</div>
</section></section>
<section>
<section id="results" class="title-slide slide level1 center">
<h1>Results</h1>
</section>
<section id="diagnostic-plots-for-model-without-transformation" class="slide level2">
<h2>Diagnostic Plots for Model <em>Without</em> Transformation</h2>
<img data-src="women-in-stem_files/figure-revealjs/unnamed-chunk-8-1.png" width="960" class="r-stretch"></section>
<section id="diagnostic-plots-for-model-with-transformation" class="slide level2">
<h2>Diagnostic Plots for Model <em>With</em> Transformation</h2>
<img data-src="women-in-stem_files/figure-revealjs/unnamed-chunk-9-1.png" width="960" class="r-stretch"></section>
<section id="metrics-comparison" class="slide level2">
<h2>Metrics Comparison</h2>
<div class="cell">
<div class="cell-output cell-output-stdout">
<pre><code># Comparison of Model Performance Indices
Name | Model | AIC (weights) | BIC (weights) | R2 | R2 (adj.) | RMSE
---------------------------------------------------------------------------------------
lm1_reduced | lm | 1618.1 (<.001) | 1632.1 (<.001) | 0.486 | 0.457 | 9393.617
lm2_reduced | lm | -1678.7 (>.999) | -1664.7 (>.999) | 0.573 | 0.549 | 3.573e-06</code></pre>
</div>
</div>
</section></section>
<section id="conclusion" class="title-slide slide level1 center">
<h1>Conclusion</h1>
<ul>
<li>Regression models with an inverse-transformation dependent response variable are not easy to explain to individuals without a statistics background, which is likely to occur in statistical consulting.</li>
<li>Based on the adjusted <span class="math inline">\(R^2\)</span> values of the two models, there is a less than 10% loss of ability to explain the variability between our response variable and explanatory variables by using a linear regression model <strong>without</strong> an inverse-transformation dependent response variable to one <strong>with</strong>.</li>
</ul>
</section>
<section id="further-research" class="title-slide slide level1 center">
<h1>Further Research</h1>
<ul>
<li>I would like to redo my analysis with a data set of a more quantitative nature, and run the regression models using the <a href="https://github.com/tidymodels">TidyModels</a> framework.</li>
<li>I would like to do a comparison of the data visualizations and analyses available in the various ggplot2 extension packages (<a href="https://github.com/kassambara/ggpubr"><code>ggpubr</code></a>, <a href="https://github.com/easystats"><code>easystats</code></a>, <a href="https://github.com/yeukyul/lindia"><code>lindia</code></a>, <a href="https://github.com/IndrajeetPatil/ggstatsplot"><code>ggstatsplot</code></a>) used in this presentation.</li>
</ul>
</section>
<section id="acknowledgements" class="title-slide slide level1 center">
<h1>Acknowledgements</h1>
<ul>
<li>I would like to thank my colleagues, Sara Hatter and Ken Vu, with whom I collaborated on the previous research projects, <a href="https://github.com/lgibson7/Gender-Wage-Inequality-in-STEM"><em>Gender Wage Inequality in STEM</em></a> and <a href="https://github.com/lgibson7/Unemployment-in-STEM"><em>Unemployment in STEM</em></a>, which laid the groundwork for this project.</li>
<li>I would like to acknowledge the FiveThirtyEight blog for uploading the data behind their story, <a href="https://fivethirtyeight.com/features/the-economic-guide-to-picking-a-college-major/"><em>The Economic Guide To Picking A College Major</em></a>, which was used for this analysis.</li>
<li>I would like to thank Prof. Eric Suess for his guidance with this research and the <strong><em>#rstats</em></strong> community members who helped with the styling of this presentation.</li>
</ul>
</section>
<section id="appendix" class="title-slide slide level1 center">
<h1>Appendix</h1>
<ul>
<li>This presentation can be viewed at: <a href="https://lgibson7.quarto.pub/women-in-stem" class="uri">https://lgibson7.quarto.pub/women-in-stem</a>.</li>
<li>Code for this presentation can be found at: <a href="https://github.com/lgibson7/Women-in-STEM" class="uri">https://github.com/lgibson7/Women-in-STEM</a>.</li>
</ul>
<div class="footer footer-default">
<p>Cal State East Bay STAT 694 Final Presentation</p>
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</section>
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// Turns fragments on and off globally
fragments: true,
// Flags whether to include the current fragment in the URL,
// so that reloading brings you to the same fragment position
fragmentInURL: false,
// Flags if the presentation is running in an embedded mode,
// i.e. contained within a limited portion of the screen
embedded: false,
// Flags if we should show a help overlay when the questionmark
// key is pressed
help: true,
// Flags if it should be possible to pause the presentation (blackout)
pause: true,
// Flags if speaker notes should be visible to all viewers
showNotes: false,
// Global override for autoplaying embedded media (null/true/false)
autoPlayMedia: null,
// Global override for preloading lazy-loaded iframes (null/true/false)
preloadIframes: null,
// Number of milliseconds between automatically proceeding to the
// next slide, disabled when set to 0, this value can be overwritten
// by using a data-autoslide attribute on your slides
autoSlide: 0,
// Stop auto-sliding after user input
autoSlideStoppable: true,
// Use this method for navigation when auto-sliding
autoSlideMethod: null,
// Specify the average time in seconds that you think you will spend
// presenting each slide. This is used to show a pacing timer in the
// speaker view
defaultTiming: null,
// Enable slide navigation via mouse wheel
mouseWheel: false,
// The display mode that will be used to show slides
display: 'block',
// Hide cursor if inactive
hideInactiveCursor: true,
// Time before the cursor is hidden (in ms)
hideCursorTime: 5000,
// Opens links in an iframe preview overlay
previewLinks: false,
// Transition style (none/fade/slide/convex/concave/zoom)
transition: 'none',
// Transition speed (default/fast/slow)
transitionSpeed: 'default',
// Transition style for full page slide backgrounds
// (none/fade/slide/convex/concave/zoom)
backgroundTransition: 'none',
// Number of slides away from the current that are visible
viewDistance: 3,
// Number of slides away from the current that are visible on mobile
// devices. It is advisable to set this to a lower number than
// viewDistance in order to save resources.
mobileViewDistance: 2,
// The "normal" size of the presentation, aspect ratio will be preserved
// when the presentation is scaled to fit different resolutions. Can be
// specified using percentage units.
width: 1050,
height: 700,
// Factor of the display size that should remain empty around the content
margin: 0.1,
math: {
mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
config: 'TeX-AMS_HTML-full',
tex2jax: {
inlineMath: [['\\(','\\)']],
displayMath: [['\\[','\\]']],
balanceBraces: true,
processEscapes: false,
processRefs: true,
processEnvironments: true,
preview: 'TeX',
skipTags: ['script','noscript','style','textarea','pre','code'],
ignoreClass: 'tex2jax_ignore',
processClass: 'tex2jax_process'
},
},
// reveal.js plugins
plugins: [QuartoLineHighlight, PdfExport, RevealMenu, QuartoSupport,
RevealMath,
RevealNotes,
RevealSearch,
RevealZoom
]
});
</script>
<script>
// htmlwidgets need to know to resize themselves when slides are shown/hidden.
// Fire the "slideenter" event (handled by htmlwidgets.js) when the current
// slide changes (different for each slide format).
(function () {
function fireSlideChanged(previousSlide, currentSlide) {
// dispatch for htmlwidgets
const event = window.document.createEvent("Event");
event.initEvent("slideenter", true, true);
window.document.dispatchEvent(event);
// dispatch for shiny
if (window.jQuery) {
if (previousSlide) {
window.jQuery(previousSlide).trigger("hidden");
}
if (currentSlide) {
window.jQuery(currentSlide).trigger("shown");
}
}
}
// hookup for reveal
if (window.Reveal) {
window.Reveal.addEventListener("slidechanged", function(event) {
fireSlideChanged(event.previousSlide, event.currentSlide);
});
}
// hookup for slidy
if (window.w3c_slidy) {
window.w3c_slidy.add_observer(function (slide_num) {
// slide_num starts at position 1
fireSlideChanged(null, w3c_slidy.slides[slide_num - 1]);
});
}
})();
</script>
<script id="quarto-html-after-body" type="application/javascript">
window.document.addEventListener("DOMContentLoaded", function (event) {
const toggleBodyColorMode = (bsSheetEl) => {
const mode = bsSheetEl.getAttribute("data-mode");
const bodyEl = window.document.querySelector("body");
if (mode === "dark") {
bodyEl.classList.add("quarto-dark");
bodyEl.classList.remove("quarto-light");
} else {
bodyEl.classList.add("quarto-light");
bodyEl.classList.remove("quarto-dark");
}
}
const toggleBodyColorPrimary = () => {
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
if (bsSheetEl) {
toggleBodyColorMode(bsSheetEl);
}
}
toggleBodyColorPrimary();
const tabsets = window.document.querySelectorAll(".panel-tabset-tabby")
tabsets.forEach(function(tabset) {
const tabby = new Tabby('#' + tabset.id);
});
const clipboard = new window.ClipboardJS('.code-copy-button', {
target: function(trigger) {
return trigger.previousElementSibling;
}
});
clipboard.on('success', function(e) {
// button target
const button = e.trigger;
// don't keep focus
button.blur();
// flash "checked"
button.classList.add('code-copy-button-checked');
var currentTitle = button.getAttribute("title");
button.setAttribute("title", "Copied!");
setTimeout(function() {
button.setAttribute("title", currentTitle);
button.classList.remove('code-copy-button-checked');
}, 1000);
// clear code selection
e.clearSelection();
});
function tippyHover(el, contentFn) {
const config = {
allowHTML: true,
content: contentFn,
maxWidth: 500,
delay: 100,
arrow: false,
appendTo: function(el) {
return el.closest('section.slide') || el.parentElement;
},
interactive: true,
interactiveBorder: 10,
theme: 'quarto-reveal',
placement: 'bottom-start'
};
config['offset'] = [0,0];
config['maxWidth'] = 700;
window.tippy(el, config);
}
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
for (var i=0; i<noterefs.length; i++) {
const ref = noterefs[i];
tippyHover(ref, function() {
// use id or data attribute instead here
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
try { href = new URL(href).hash; } catch {}
const id = href.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
return note.innerHTML;
});
}
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const cites = ref.parentNode.getAttribute('data-cites').split(' ');
tippyHover(ref, function() {
var popup = window.document.createElement('div');
cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
});
</script>
</body></html>