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Week5_GLM2.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="author" content="Joshua F. Wiley / Michelle Byrne / Pei Hwa Goh" />
<meta name="date" content="2025-03-29" />
<title>Generalized Linear Models 2</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
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<h1 class="title toc-ignore">Generalized Linear Models 2</h1>
<h4 class="author">Joshua F. Wiley / Michelle Byrne / Pei Hwa Goh</h4>
<h4 class="date">2025-03-29</h4>
<div id="TOC">
<ul>
<li><a href="#setup" id="toc-setup"><span class="toc-section-number">1</span> Setup</a></li>
<li><a href="#generalized-linear-models" id="toc-generalized-linear-models"><span class="toc-section-number">2</span> Generalized Linear Models</a></li>
<li><a href="#poisson-regression" id="toc-poisson-regression"><span class="toc-section-number">3</span> Poisson Regression</a>
<ul>
<li><a href="#poisson-regression-assumptions" id="toc-poisson-regression-assumptions"><span class="toc-section-number">3.1</span> Poisson Regression Assumptions</a></li>
<li><a href="#poisson-regression-in-r" id="toc-poisson-regression-in-r"><span class="toc-section-number">3.2</span> Poisson Regression in <code>R</code></a>
<ul>
<li><a href="#poisson-regression-interpretation" id="toc-poisson-regression-interpretation"><span class="toc-section-number">3.2.1</span> Poisson Regression Interpretation</a></li>
</ul></li>
</ul></li>
<li><a href="#binary-logistic-regression" id="toc-binary-logistic-regression"><span class="toc-section-number">4</span> Binary Logistic Regression</a>
<ul>
<li><a href="#logistic-regression-assumptions" id="toc-logistic-regression-assumptions"><span class="toc-section-number">4.1</span> Logistic Regression Assumptions</a></li>
<li><a href="#logistic-regression-in-r-part-1" id="toc-logistic-regression-in-r-part-1"><span class="toc-section-number">4.2</span> Logistic Regression in <code>R</code> Part 1</a>
<ul>
<li><a href="#logistic-regression-interpretation" id="toc-logistic-regression-interpretation"><span class="toc-section-number">4.2.1</span> Logistic Regression Interpretation</a></li>
</ul></li>
<li><a href="#logistic-regression-in-r-part-2" id="toc-logistic-regression-in-r-part-2"><span class="toc-section-number">4.3</span> Logistic Regression in <code>R</code> Part 2</a>
<ul>
<li><a href="#average-marginal-effects" id="toc-average-marginal-effects"><span class="toc-section-number">4.3.1</span> Average Marginal Effects</a></li>
</ul></li>
<li><a href="#glms-with-multiple-predictors" id="toc-glms-with-multiple-predictors"><span class="toc-section-number">4.4</span> GLMs with Multiple Predictors</a></li>
</ul></li>
<li><a href="#using-a-function" id="toc-using-a-function"><span class="toc-section-number">5</span> Using a Function</a></li>
<li><a href="#summary-table" id="toc-summary-table"><span class="toc-section-number">6</span> Summary Table</a></li>
<li><a href="#bonus-content" id="toc-bonus-content"><span class="toc-section-number">7</span> Bonus Content</a></li>
</ul>
</div>
<div id="setup" class="section level1" number="1">
<h1><span class="header-section-number">1</span> Setup</h1>
<p>You can download the <code>R</code>markdown file for this content from the GitHub folder
for this unit.</p>
<p>We will be using a few packages for this content and also the baseline
data only from the data collection exercise.</p>
<pre class="r"><code>options(digits = 3)
library(haven)
library(data.table)
library(JWileymisc)
library(ggplot2)
library(ggpubr)</code></pre>
<pre><code>##
## Attaching package: 'ggpubr'</code></pre>
<pre><code>## The following object is masked from 'package:ggplot2':
##
## theme_transparent</code></pre>
<pre class="r"><code>library(visreg)
library(survey)</code></pre>
<pre><code>## Loading required package: grid</code></pre>
<pre><code>## Loading required package: Matrix</code></pre>
<pre><code>## Loading required package: survival</code></pre>
<pre><code>##
## Attaching package: 'survey'</code></pre>
<pre><code>## The following object is masked from 'package:graphics':
##
## dotchart</code></pre>
<pre class="r"><code>library(marginaleffects)
## read in data
db <- as.data.table(read_sav("[2021] PSY4210 BL.sav")) # baseline
## if you have saved your last db datafile as an RData, simply go
## to the files tab on the bottom right corner of your window and
## click on it to load your saved db datafile here
## compute a stress variable if you haven't already
db [, PSS2 := 6 - PSS2r]
db [, PSS3 := 6 - PSS3r]
db[, stress := rowMeans(.SD, na.rm = TRUE) * 4,
.SDcols = c("PSS1", "PSS2", "PSS3", "PSS4")]
## compute a self-esteem variable if you haven't already
db[, selfesteem := rowMeans(.SD, na.rm = TRUE),
.SDcols = c("LSE1", "LSE2", "LSE3", "LSE4")]
## compute a neuroticism variable if you haven't already
db [, N1 := 6 - BFI_N1r]
db[, neuroticism := rowMeans(.SD, na.rm = TRUE),
.SDcols = c("N1", "BFI_N2")]
## create some binary variables
db[, StressHigh := as.integer(stress >= 10)]
db[, SelfesteemHigh := as.integer(selfesteem >= 3.75)]
## read in some example data from the internet
## (requires internet connection to run)
dcount <- fread("https://stats.oarc.ucla.edu/stat/data/poisson_sim.csv")</code></pre>
</div>
<div id="generalized-linear-models" class="section level1" number="2">
<h1><span class="header-section-number">2</span> Generalized Linear Models</h1>
<p>We previously learned about linear regression and how it fit into the
Generalized Linear Models (GLM) framework.</p>
<p>Now we are going to learn about two other special cases of GLMs:
binary logistic regression and poisson regression.</p>
</div>
<div id="poisson-regression" class="section level1" number="3">
<h1><span class="header-section-number">3</span> Poisson Regression</h1>
<p>Poisson regression is used when the outcome is a count variable. Count
variables are discrete and must be whole, 0 or positive numbers (e.g.,
0, 1, 2, 3, etc.). The poisson distribution is used most often when
the counts are relatively rare. Some examples of research use cases
where a poisson may be appropriate are:</p>
<ul>
<li>examining risk factors for the number of accidents someone gets into
over a 12 month period</li>
<li>analysing the number of children people have</li>
<li>predicting how many friends people have</li>
<li>evaluating whether an intervention reduced the number of times
someone missed their medication in the last month</li>
<li>testing whether the total number of health care appointments over
six months can be lowered by treating mental health</li>
</ul>
<p>For count variables, it is common and not necessarily a problem if
most people score a 0, with relatively few people having counts of 1,
2, 3, etc.</p>
<p>In the simulated <code>dcount</code> data we downloaded from the internet, there
is a variable, <code>num_awards</code> which is the number of awards a student
got. We can use <code>testDistribution()</code> to examine this and get a default
comparison against a normal distribution as shown in the following
figure. The density plot is “lumpy” showing the discrete nature of the
data. No transformation would make this data approximately normally
distributed.</p>
<pre class="r"><code>plot(testDistribution(dcount$num_awards))</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<p>Rather than transform the data, we can change the distribution. We
again use <code>testDistribution()</code> but this time specify the distribution
as “poisson”. The poisson distribution is a discrete distribution so
a continuous density curve is not plotted. Instead, we get discrete
bars where the solid dark grey bars show the observed density of
different values and the blue bars show the density under a poisson
distribution. The deviaties plot at the bottom again shows deviations
from the assumed distribution, in this case, the poisson. Although the
densities are not a perfect match, they are relatively close and we
can see from the log likelihood values (labelled <code>LL</code>) printed in the graphs that
the poisson has a <strong>much</strong> higher log likelihood for the data than
does the normal distribution we tried earlier.</p>
<pre class="r"><code>plot(testDistribution(dcount$num_awards, distr = "poisson"))</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<p>Like the normal distribution, the poisson distribution is a family of
distributions and the specific one you will get is controlled by a
single parameter, <span class="math inline">\(\lambda\)</span>, which is both the mean and the variance
of the poisson distribution. You can find out more about the poisson
distribution
<a href="https://en.wikipedia.org/wiki/Poisson_distribution">here</a>
including the relevant equations for it. The figure that follows shows
the density for different counts under a poisson distribution with
varying <span class="math inline">\(\lambda\)</span> values.</p>
<p><img role="img" 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" width="576" /></p>
<p>Linear regression rarely works well for count outcomes for two reasons:</p>
<ul>
<li>First, when an outcome can only be 0 or positive whole numbers, a
straight line often is a bad fit and certainly at extremes (e.g.,
negative values) is impossible.</li>
<li>Second, unless the average number of counts is fairly high, a count
variable and its residuals will not follow anything approximating a
normal distribution: the normality assumption would be violated.</li>
</ul>
<p>The GLM solves each of these problems separately</p>
<ul>
<li>Link functions transform the linear predicted value <span class="math inline">\(\eta\)</span> so that
it never goes below 0</li>
<li>Rather than assume a normal distribution, the GLM can assume a
poisson distribution
<ul>
<li>Whereas the Normal distribution had two parameters, mean and
standard deviation, the poisson distribution only has one: the
average which is the same as the variance, called <span class="math inline">\(\lambda\)</span></li>
</ul></li>
</ul>
<p>For poisson regression, the link function is defined as:</p>
<p><span class="math display">\[ \eta = g(\lambda) = ln(\lambda) \]</span></p>
<p>where <span class="math inline">\(ln()\)</span> is the <strong>n</strong>atural <strong>l</strong>ogarithm (or log with base e,
euler’s number).</p>
<p><label for="tufte-mn-1" class="margin-toggle">⊕</label><input type="checkbox" id="tufte-mn-1" class="margin-toggle"><span class="marginnote">Although lambda can be exactly 0, here lambda is the average number of counts / events. Although
counts must be at least 0 and strictly whole numbers, the average number of
counts, lambda can be any real, positive number number > 0.</span></p>
<p>Graphing <span class="math inline">\(\lambda\)</span> against <span class="math inline">\(\lambda\)</span> we get</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 1a. Average counts against average counts
</p>
<img role="img" aria-label="Fig 1a. Average counts against average counts" src="data:image/png;base64,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" alt="Fig 1a. Average counts against average counts" width="576" />
</div>
<p>The link function, the natural logarithm, unbounds <span class="math inline">\(\lambda\)</span> on the
left side because the log of 0 is negative infinity</p>
<p>The following graph shows the raw <span class="math inline">\(\lambda\)</span> values against the
natural log transformed values.</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 1b. Average counts against log transformed average counts
</p>
<img role="img" aria-label="Fig 1b. Average counts against log transformed average counts" src="data:image/png;base64,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" alt="Fig 1b. Average counts against log transformed average counts" width="576" />
</div>
<p>In this way, the link function for poisson regression takes the
average number of counts, which can only fall > 0 and transforms it to
fall between negative infinity and positive infinity</p>
<p>Now we have a continuous and unbounded outcome we can apply
a linear model to!</p>
<p>To go from predictions on the linear model back to the original
count scale, we use the inverse link function:</p>
<ul>
<li><span class="math inline">\(\lambda = g^{-1}(\eta) = e^{\eta}\)</span></li>
</ul>
<p>That is, suppose we had the linear predicted values, <span class="math inline">\(\eta\)</span> shown
below graphically</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 2a. Linear predictor against linear predictor
</p>
<img role="img" aria-label="Fig 2a. Linear predictor against linear predictor" src="data:image/png;base64,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" alt="Fig 2a. Linear predictor against linear predictor" width="576" />
</div>
<p>Using the inverse link function, we transform them to again fall
> 0.</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 2b. Linear predictor (log scale) against average counts
</p>
<img role="img" aria-label="Fig 2b. Linear predictor (log scale) against average counts" src="data:image/png;base64,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" alt="Fig 2b. Linear predictor (log scale) against average counts" width="576" />
</div>
<div id="poisson-regression-assumptions" class="section level2" number="3.1">
<h2><span class="header-section-number">3.1</span> Poisson Regression Assumptions</h2>
<p>Much like a normal distribution was assumed for normal linear
regression, for poisson regression a poisson distribution is
assumed.</p>
<p><span class="math display">\[ y \sim Pois(\lambda) \]</span></p>
<p>In poisson regression although for relatively less common outcomes,
outliers on the left hand side may not be a concern, large positive
outliers (e.g., someone with an extreme number of awards, or who has
multiple health appointments daily, etc.) may be a concern.</p>
<p>Outliers on predictors may still be a concern.</p>
<p>Poisson regression still requires that the errors be independent
(i.e., individuals are independent, not dependent or repeated
measures).</p>
<p>Poisson regression also assumes that on the link scale (natural log scale)
there is a linear relationship.</p>
<p>Finally, poisson regression generally requires a large sample size.
There are no degrees of freedom so it requires a large enough sample
that <strong>parameters</strong> are distributed about normally relying on the
central limit theorem.</p>
</div>
<div id="poisson-regression-in-r" class="section level2" number="3.2">
<h2><span class="header-section-number">3.2</span> Poisson Regression in <code>R</code></h2>
<p>To estimate a poisson regression in <code>R</code>, we can use the <code>glm()</code>
function which allows us to fit a variety of different GLMs, including
poisson regression. <code>glm()</code> works almost identically to <code>lm()</code>, with a
few caveats. The first caveat is that for anything other than a linear
model, we need to specify the <code>family =</code> argument, which controls
which specific type of GLM is estimated. In this case we want a
poisson regression, so we use <code>family = poisson()</code>.</p>
<p>The second caveat is that although some functions we are used to from
working with <code>lm()</code> will carry over to working with <code>glm()</code> models,
many functions will not work or will not work the same way. Because
linear regression is the most common, there tend to be the most tools
and convenience features implemented for it. In addition, some things,
like <span class="math inline">\(R^2\)</span> variance explained that makes sense with linear regression
does not really make sense for poisson regression.</p>
<p>The following code fits a poisson regression to the number of awards
<code>num_awards</code> predicted by math scores, <code>math</code>. There is not a single
agreed upon way to evaluate the residuals of these models for whether
they meet the assumptions, so we may just evaluate the distribution of
the outcome to see if it closely fits a poisson distribution.
The figure suggests its fairly close, so we might proceed with a
summary of the model from <code>summary()</code>.</p>
<pre class="r"><code>m <- glm(num_awards ~ math, data = dcount, family = poisson())
plot(testDistribution(dcount$num_awards, distr = "poisson"))</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<pre class="r"><code>summary(m)</code></pre>
<pre><code>##
## Call:
## glm(formula = num_awards ~ math, family = poisson(), data = dcount)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.33353 0.59126 -9.02 <2e-16 ***
## math 0.08617 0.00968 8.90 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 287.67 on 199 degrees of freedom
## Residual deviance: 204.02 on 198 degrees of freedom
## AIC: 384.1
##
## Number of Fisher Scoring iterations: 6</code></pre>
<p>The output from <code>summary(m)</code> is fairly similar to what we would see
for a linear regression in <code>R</code>.</p>
<ul>
<li>Deviance Residuals: these still represent model residuals, but they
are no longer raw residuals defined as <span class="math inline">\(y - \hat{y}\)</span>. Deviance
residuals are how much each data point contributed to the residual
deviance, a sort of measure of overall model fit. They are analogous
to residuals in linear regression, in that when you sum and square
these residuals, you get the sums of squares used to assess model
fit. They differ in that they are not calculated as the raw
difference between each data point and the predicted value.</li>
<li>Coefficients: the coefficients table is interpreted nearly
identically as in linear regression. The estimates are the
regression coefficients, the standard errors are given next. Instead
of t values, z values are presented because in general for GLMs we
cannot calculate degrees of freedom so we rely on the central limit
theory, and so instead of a t-test, we use a z-test (recall from
early stats that with an infinite sample size, the t-distribution
becomes identical to the normal distribution and thus the t-test and
z-test are the same, with an infinite sample and they are
functionally the same with a relatively large sample). P values are
in the final column, now based of the z-test instead of the t-tests
used in linear regression.</li>
<li>There is no model <span class="math inline">\(R^2\)</span> as that only works clearly for linear
regression. Instead, we get null and residual deviance values and an
AIC, which stands for the Akaike Information Criterion, a relative
measure of model fit taking into account model complexity. We’ll
learn more about this much later in the semester, for now you don’t
need to worry about them.</li>
<li>The number of Fisher scoring iterations. This is included because
unlike linear regression where we can directly calculate the best
parameter estimates. For other GLMs, the computer tries different
values and finds the best values, in a process known as
optimization. At each step of the optimization it evaluates how well
the specific parameter estimates work and based on some criteria
whether to keep trying for better estimates or stop trying. Each one
of these steps is called an “iteration” and the number of iterations
can give a rough sense of how hard it was for the computer to find
the values. Again you can mostly ignore these for now, although it
will become more important as we talk about mixed effects models.</li>
</ul>
<div id="poisson-regression-interpretation" class="section level3" number="3.2.1">
<h3><span class="header-section-number">3.2.1</span> Poisson Regression Interpretation</h3>
<p>At one level, we can interpret the coefficients for poisson regression
nearly identically to those for linear regression, as long as we use
the log scale. An example follows.</p>
<p>A poisson regression predicting the number of awards each student
received from their math scores showed that students who had a 0 math
score were expected to have
-5.33 log awards,
p < .001.
Each one unit higher math score was associated with
0.09 higher log awards,
p < .001.
A graph of these results follows.</p>
<pre class="r"><code>visreg(m, xvar = "math", partial = FALSE, rug = FALSE, gg = TRUE) +
ylab("predicted log number of awards") +
theme_pubr()</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<p>By specifying that we are working on a log scale, we can interpret the
results as we did before and graph the results almost the same as
before, other than needing to mention the log. Although these
interpretations are technically accurate, for most people, it is hard
to understand results on a log scale.</p>
<p>If we exponentiate the regression coefficients, specifically the
slopes, we get what are called <strong>Incident Rate Ratios</strong> or IRRs.
IRRs indicate how many more times the outcome will be for a one unit
change in the predictor. For example, if the <span class="math inline">\(IRR = 2\)</span> and the base
rate was 1, then one unit higher would be <span class="math inline">\(1 * 2 = 2\)</span>. If the base
rate was 2, then a one unit higher would be <span class="math inline">\(2 * 2 = 4\)</span>.
IRRs are interpreted as for each one unit higher predictor score,
there are IRR times as many events of the outcome. Because IRRs are
multiplicative, an IRR of 1 means that a one unit change in the
predictor is associated with 1 times as many events on the outcome,
that is no change. Thus on the IRR scale, a coefficient of 1 is
equivalent to a coefficient of 0 on the link (log) scale.</p>
<p>Note that although we can exponentiate coefficients, confidence
intervals, or predictions, we should <em>not</em> exponentiate standard
errors, z values or p values. To get the IRRs in <code>R</code>, we can extract
the coefficients from the model using the <code>coef()</code> function and then
exponentiate using the <code>exp()</code> function and we follow a nearly
identical process for the confidence intervals.</p>
<pre class="r"><code>exp(coef(m))</code></pre>
<pre><code>## (Intercept) math
## 0.00483 1.08999</code></pre>
<pre class="r"><code>exp(confint(m))</code></pre>
<pre><code>## Waiting for profiling to be done...</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) 0.00147 0.015
## math 1.06970 1.111</code></pre>
<p>We can interpret poisson regression using the IRRs as follows.</p>
<p>A poisson regression predicting the number of awards each student
received from their math scores showed that students who had a 0 math
score were expected to have
0.00 awards,
[95% CI 0.00 - 0.01].
Each one unit higher math score was associated with having
1.09 times the number of
awards,
[95% CI 1.07 - 1.11],
p < .001.
A graph of these results follows.</p>
<pre class="r"><code>visreg(m, xvar = "math", scale = "response",
partial = FALSE, rug = FALSE, gg = TRUE) +
ylab("predicted number of awards") +
theme_pubr()</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<p>Note that when calling <code>visreg()</code>, we added the new argument, <code>scale = "response"</code>. This tells <code>R</code> that we do not want the results on the
linear link scale, we want them on the original response scale. This
argument for <code>visreg()</code> is helpful any time you are working with non
linear link functions. The figure also shows how although on the link
scale there was a perfectly linear model prediction, the linear model
on the original response scale is clearly not linear.</p>
<p>Poisson regression with multiple predictors follows the same
interpretation, but just as with linear regression you need to specify
that what is being evaluated is the unique / independent association
of each predictor with the outcome, independent of other variables in
the model.</p>
</div>
</div>
</div>
<div id="binary-logistic-regression" class="section level1" number="4">
<h1><span class="header-section-number">4</span> Binary Logistic Regression</h1>
<p>Binary logistic regression is regression when the outcome only takes
on two values: 0 or 1. Logistic regression is useful for many
questions, such as:</p>
<ul>
<li>What predicts whether someone will have major depression or not?</li>
<li>Does one treatment have a higher probability of patients <em>remitting</em>
from major depression than another treatment?</li>
<li>What is the probability that a patient will be re-admitted to the
hospital within 30 days of discharge?</li>
<li>What predicts whether an individual will live or die before age 60?</li>
<li>If a bank gives a loan to someone, what is their probability of not
being able to pay it back?</li>
<li>Do older adults have a higher probability of using CAM than younger
adults?</li>
</ul>
<p>Linear regression will not work for binary outcomes for two reasons:</p>
<ul>
<li>First, when an outcome can only be 0 or 1, a straight line is a very
bad fit
<ul>
<li>straight lines could predict a value of 1.4 or 2 or -0.3 when
those values are not possible</li>
</ul></li>
<li>Second, there is no way that a binary variable or its residuals will
follow a normal distribution: the normality assumption would be
violated</li>
</ul>
<p>The GLM solves each of these problems separately</p>
<ul>
<li>Link functions transform the linear predicted value <span class="math inline">\(\eta\)</span> so that
it never goes below 0 and never goes above 1</li>
<li>Rather than assume a normal distribution, the GLM uses a new
distribution, the Bernoulli distribution
<ul>
<li>Whereas the Normal distribution had two parameters, mean and
standard deviation, the Bernoulli distribution only has one: the
average probability that an event will occur, sometimes <span class="math inline">\(p\)</span> or <span class="math inline">\(\mu\)</span></li>
</ul></li>
</ul>
<p>For logistic regression, the link function is defined as:</p>
<p><span class="math display">\[ \eta = g(\mu) = ln\left(\frac{\mu}{1 - \mu}\right) \]</span></p>
<p>That is called the <em>logit</em> function.</p>
<p>Here <span class="math inline">\(\mu\)</span> is the probability that the outcome will
be 1. Probabilities range from 0 to 1: an outcome cannot happen less
than never (probability of 0) or more than always (probability of 1).</p>
<p>Graphing <span class="math inline">\(\mu\)</span> against <span class="math inline">\(\mu\)</span> we get</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 1a. Probabilities against Probabilities
</p>
<img role="img" aria-label="Fig 1a. Probabilities against Probabilities" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABIAAAAMACAMAAABrYew+AAAArlBMVEUAAAAAADoAAGYAOjoAOmYAOpAAZrYzMzM6AAA6OgA6Ojo6OmY6ZpA6ZrY6kNtmAABmOgBmOjpmZjpmZmZmZpBmkLZmkNtmtrZmtttmtv+QOgCQZgCQZjqQZmaQttuQ29uQ2/+2ZgC2Zjq2kDq2kGa2tpC2ttu229u22/+2///bkDrbkGbbtmbbtpDb27bb29vb2//b/9vb////tmb/25D/27b/29v//7b//9v///+p655jAAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO3d62Ijx7UeUFA3M9ZIM/aJFFHRUcTEOZKoi53hjId8/xcLQDaARt8GbPRlV9Vaf0wDPWR1196fCtUguHkEWMlm7QEA5RJAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABqxFAwGoCBNAmwBiANQRofgEEpQrQ/AIIShWg+QUQlCpA8wsgKFWA5hdAUKoAzS+AoFQBml8AQakCNL8AglIFaH4BBKUK0PwCCEoVoPkFEJQqQPMLIChVgOYXQFCqC5v/w+tPfu14+P0P15vN1atfhh45DkEAQaEua/6H7zddAfT7Nmx2rr7tf6Q2BAEEhbqo+R9uN10BdL85uOl7pD4EAQSFuqT5t+ufrgD68Hqz+Wz7WuvPN/tn24+cDEEAQaEuaP4/nl5WtQPlbrP5/O3ui11Afd39yMkQBBAUanTzv9+uZjav3rQDaBsyVz89f/nu+il42o+cDkEAQaFGN/92VXP1Xdcm9Pb11j5jquRpP3I6BAEEhRofQFdfve28C3a/2Xyx//r2adO5/cjpEAQQFGp08/97t6bpCaDDNs/dPoAaj5wOQQBBoaZ/H1A9Yp6jp/3Is79UBBAUSgABqxFAwGhP7y6+5N9f9NMvC6D9EAQQJOnwCw7jv8NFP18AQcEiBpC7YFCG4694ju7hWQLI+4CgACEDyDuhoQibkAHkd8Egd8+hEzKA/DY85G3TNvpbXTSQzgB6+vSfn1ufB/SzzwOCLEyXPxMG0DZlqhdaPhERMjbhAmiWAHr8rfUJ0O1HakMQQJCQevBcFj8zBZC/igHZmmTlc/hmEwzo0iEEGAPwUVXmCCBgaR1bPwIIWEZj42eS/BFAwDlmWQAJIOAcJ7kzUfwIIOAc0y58jt92wu81dggBxgD0aWz8CCBgKbNs/Ry/+4Tfa+wQAowB6DZr/gggYMC8CyABBAyoB8/k8SOAgAFzrXwO33+Ob/rCIQQYA9Aw582v4w+Z45u+cAgBxgCcmHnv5/Bj5vimLxxCgDEAJ5bJHwEEtC20ABJAQNvMN7+OP2em7/uSIQQYA1Az+8rn8INm/e7nDSHAGIAnVeYIIGBpHVs/AghYRmPjZ/b8EUDA3uILIAEE7J3kzgLxI4CAveUWPscfudDPGRpCgDEAy937qv3EhX7O0BACjAHK1th5FkDAUpbeeq795KV+0MAQAowBSiaAgLXUg2fR+BFAwAorn8OPXvoHdgwhwBigXGu89Dr87KV/YMcQAowBirTWza/jAJb+gR1DCDAGKFB771kAAQtZP38EEJQqwAJIAEGpVrz7fhzDCj+zOYQAY4DirLryOQxitZ98HEKAMUBBqswRQM9DCDAGKEbH1o8AApbR2PhZNX8EEJQl1AJIAEFZTnJn5fgRQFCWGAufgwBjCHEdIHuNjZ8QjRdgDCGuA2Qu1NbPQYAxhLgOkLmQ+SOAoAgxF0ACCIpQD54w8SOAoAjRVj57AQYT64JAZiLe/DoIMJhYFwSyEnTvZy/AYGJdEMhK7PwRQJCz4AsgAQQ5C3rz6yDAeMJdE8hF2JXPXoBRBb0ykLIqcwTQx4cQYAyQlY6tn5htFmBUQa8MpKux8RM2fwQQ5CeZBZAAgvyc5E7g+BFAkJ/4C5+DAOMLf40gGY2Nn/DNFWB84a8RJCKZrZ+DAOMLf40gEcnljwCCbKS3ABJAkI168CQRPwIIspHSymcvwEDTuVgQVGo3vw4CDDSdiwUhJbj3sxdgoOlcLAgp3fwRQJC6hBdAAghSl+DNr4MAY03qekE0Sa589gKMOMGrBhFUmSOALhtCgDFAcjq2ftJrpQAjTvCqwfoaGz9J5o8AgjRlsQASQJCmk9xJNH4EEKQp7YXPQYCxJ339YHGNjZ+kGyjA2JO+frCwLLZ+DgKMPenrBwvLKn8EECQlrwWQAIKk1IMn+fgRQJCUXFY+ewFOIo8LCTPL6ebXQYCTyONCwqwy2/vZC3ASeVxImFWe+SOAIAWZLoAEEKQgs5tfBwHOI5trCXPJbuWzF+BsMruiMKUqcwTQfEMIMAYIqWPrJ692CXA2mV1RmE5j4ye7/BFAEFf2CyABBHGd5E6G8SOAIK58Fz4HAc4r22sLozU2frJtkgDnle21hZGy3/o5CHBe2V5bGKmY/BFAEE45CyABBOHUgyfr+BFAEE4JK5+9ACeY/0WGM5Vy8+sgwAnmf5HhLAXt/ewFOMH8LzKcpbz8EUAQRYELIAEEURR08+sgwDkWcZ3hY4pa+ewFONOCrjZ0qTJHAK0zhABjgNV0bP2U0xIBzrSgqw1tjY2fovJHAMG6il4ACSBY10nuFBY/AgjWVebC5yDAORd53aEigNYeQoAxwPIaO89FNkKAcy7yulO8kreejwKcdJkXntIJoJ0AJ13mhadw9eApNn4EEKyj8JXPXoCTL3sCKFPpL732Apx82RNAcdz8qglw8mVPAIVp7z0XXf8BTr7sCaAw8udEgLMvfAYoigXQqQBnX/gMUBR3308FOP/i54ByWPk0BLgKZoISuPnV5YKr8P6H683m6tUvjYfvTl/gfr177OH74wM3rSGYCbJn76fb+Kvw+/XzZbz69vTxrgD68FoAUTT50230Zbjvi5SuAKodLIAokAVQj7GXYbem+Wz76uvPN5vNJ7/2HLTNoi/2X9z0D8FUkLt68IifmrEXYhspn7/dfbHb3vm6+5j7/TGPt/0hJYDIn5VPn5GXYxs7Vz89f/nueh8zDdtFUnXM9ujuQ56HYErIVpU5AqjHyMuxDZd9pNSy6NTtYWm0PfqLgSGYEjLVsfWj2k+MvBz3m2Ok3HZv8BxfgO2+vHn/t+21//LHriGYEjLV2PiRPy3jA+iw8dO9w1xfGN1trv5eXf5X7Zdi5oRMWQB91MjrUQ+d+85d6LvTNdJBbTPoLxVzQp5Ockf8dJkrgI470M83yq6+ebt77/SmfqwAImsWPh83VwDVN4lqYXRXf9eQACJXjY0fAdRnpgDquzW2WwzdNB4zOWTG1s/ZZgqg3jcH3bUPNjlkRv6cbaa7YB050/6H+yGYHbJiAXS+ed4H1PvmRAFE/urBI36GzfNO6N5XYF3LJfNDVqx8XmCe3wU7fQVW+3/1u/OHIZglMuHm10vN89vwtycxs42o6t77w+2m/VthZok82Pt5uYs+D+jnns8D2oZS/bGnNyJ+9/b54PbekFkiD/Ln5ab7RMTaq6vaDtGTd9fHg9s3x0wTWbAAGmH8Jfqt8ZnQtQBqbQu9e7M5PfhkCKaJHLj5NcJ0fxXjNIAaOz0Pf+w+jePTb/7VNQQTRQasfMYIcKlMF2mrMkcAjRDgUpkuUtax9aOizxbgUpkuUtbY+JE/LxLgWpkvEmYBdJEA18p8kbCT3BE/LxXgapkx0mXhc5kAF83EkaTGxo86HiPARTNxJMjWzyQCXDQTR4LkzyQCXDUzR3osgKYR4KqZOdJTDx7xM16A62buSI6Vz0QCXD0zSErc/JpSgKtnBkmHvZ9pBbh6ZpB0yJ9pBbh8ppBkWABNLMDlM4Ukw82viQW4gCaRVFj5TC3AZTSVxFdljgCaWIDLaCqJrmPrR9VOIsBlNJVE19j4kT+TCXAdzSXBWQDNJsB1NJcEd5I74mdKAa6k2SQ2C5/5BLigJpWwGhs/anVqAS6oSSUoWz+zC3BBTSpByZ/ZBbiiZpWYLIDmF+CKmlViqgeP+JlHgGtqXgnJymcBAa6s2SUaN7+WEuDKml1isfeznABX1uwSi/xZToBLa3oJxQJoQQEureklFDe/FhTg4ppgIrHyWVKAS2yaiaHKHAG0oACX2DQTQcfWj8qcXYBLbJqJoLHxI38WEeAam2cCsABaRYBrbJ4J4CR3xM9SAlxlM836LHzWEeBim3BW1dj4UY9LCnCxTTgrsvWzqgAX24SzIvmzqgBX24yzHgugdQW42mac9dSDR/wsL8D1NuesxspnZQGuuplnDW5+RRDgqpt5lmfvJ4YAV93Mszz5E0OAy27qWZwFUBABLrupZ3FufgUR4MKbfJZm5RNFgMuvBFhOlTkCKIgAl18JsJSOrR/Vt6oAl18JsJTGxo/8WV2A668GWIgFUDgBrr8aYCEnuSN+IggwA6qAZVj4xBNgIhQDCxFA4QSYCMXA7Bo7z2ouigAToRiYma3nsALMhGpgZgIorAAzoRqYVz14xE8sAeZCPTAvK5+4AsyIqmBWXnoFFmBGVAVzcfMrugAzoiqYR3vvWalFE2BGVAXzkD/xBZgSZcEsLIASEGBKlAWzcPc9AQEmRWEwByufFASYGuXBtKrMEUAJCDA1yoMpdWz9qLCwAkyN8mBKjY0f+RNagLlRH0zIAigpAeZGfTChk9wRP9EFmB0VwnQsfNISYJIUCpNobPyoqxQEmCSFwgRs/SQpwCQpFCYgf5IUYJZUCpezAEpTgFlSKVyuHjziJx0B5kmtcDErn0QFmC0VwyXc/EpZgNlSMYxn7ydtAWZLxTCe/ElbgOlSMoxmAZS4ANOlZBjNza/EBZgwRcNYVj6pCzBtSoeXqzJHACUuwLQpHV6qY+tHFSUpwLQpHV6qsfEjf5IVYN7UDi9kAZSNAPOmdnihk9wRPykLMHOqh5ex8MlHgAlURJytsfGjdlIXYAIVEWey9ZOdABOoiDiT/MlOgBlURZzHAig/AWZQFXGeevCInzwEmEN1xFmsfDIUYCZVEx/j5leuAsykamKYvZ98BZhJ1cQw+ZOvAFOpnBhkAZSxAFOpnBjk5lfGAkymgmKIlU/OAkypsqJblTkCKGMBplRZ0aVj60elZCfAlCorujQ2fuRPlgLMqbqigwVQEQLMqbqiw0nuiJ9cBZhVlUWbhU8ZAkyuAuNEY+NHfeQswOQqMGps/RQlwOQqMGrkT1F6ZvfhP//j1H9/O98QVBgHFkBl6ZndD68bRfDJr/MNQYVxUA8e8ZM/AUQkVj6F6Zvlf/9z7//+sLn67p//mnEIKo1HN7/KdM4sv7vefDfnEFQa9n4KddYs322ufppxCCoNN78KddY0b5dAX8w4BKWGBVChzprmD69tQjMrN78Kde4KSAAxIyufUp25B7T53BsRmUOVOQKoUB+f7od//p9tVXTsAb3/4XqzuXr1S/tffH+sppuPHSyAStax9aMainLmGxE77oL9fl099e3QP7752MECqGSNjR/5U5zzAuiq/T6g+/Yqp+Op6rmBgwVQwSyAitcXQH/769GX37TfB71LqM+2L6j+fNP+NY27ZswMHSyACnaSO+KnRGNn/LAvvdvw+fr0udtmygwdLIDKZeHDyInfJsl+W+jddeMW2fa51gO9Bz8KoCI1Nn7UQKlGTvz2RdU+SGrxcnjui7MPfhRABbL1Q2XkxN/XbszfNrZ8ts/dvP/btqa+/PHjBz8KoALJHyr9M//wx3/2fyLifW0vp7nnfLe5+ntVVq/efuzgRwFUHgsg9npnfv/OnUp7W/lm//V9Y2P5tvbPnl569R38l4rqK0w9eMRP2frm/n5z6vwA2t3puvrm7e7Nz5vnZwQQdVY+HPRVwG4Z8+q/Dh+L2PxExIEA+vD6sM989xxcAoiKm1+cGngndOsNOzVDL8GOdouhm48erApLYe+Hpv4AGvwAjvMCaHfY1wKIivyhqe/vgn0/HEAfubF1epi7YOxYANHSvwc0+DHQH3lrT+2wr70PiGduftHSVwSttzO3nh56c/Pe83rHO6F5dPOLLr2l8O5681X/pyAO/HrX3fEFV3VDzO+Clc7NL3r0l8L7N5vNp8eP5Gh/5EbPL7gfP0D64bZ67eW34Ytm74deQyuguuaW9NNH/Pzc9RE/T29E/O7t81PPK5/+g5+GoBzzJn/o1VcLjfxp50brQw4Pb0Cs/9Ovew4+GYJ6zJoFEP0G3gl99c0/e98JvfVb42Oej++Afvdmc/pU++CTIajHrNWDR/xwauCd0Dcf+aeNP3RR+xWMhz92n8bxaf2TXP1VjFJZ+TBg5DuhJx2CusyaAKLfyHdCTzoEdZmnKnMEEP36amLg9ysmH4K6zFFj40f+0KWvKFqfLD/jEBRmjgQQZ+gtim0C7d66s8QQFGaGTl54iR96DPxhwqeq6Xsn9JRDUJoZsvPDOc782/Bzbkmr0Ay5+c5ZBBATa2z8mF4GBKgOFZqTTdvaQyKwANWhQnMif3iJAOWhRDNiAcSLBCgPJZqRevCIHz4qQIEo0nxY+fAyAcpEqWbBzS9GCFAmSjUD9n4YJUCZKNUMyB9GCVAnajV9FkCME6BO1Gr63PxinACVolqTZ+XDSAHqRc0mrMocAcQ4AepFzSarY+vHZPISAepFzSarsfEjf3ipAAWjaFNlAcSlAhSMok3VSe6IH0YIUDLKNlEWPlwsQOWo3vQ0Nn5MISMFqBzVmxpbP0wlQOWo3tTIH6YSoHSUb2IsgJhMgNJRvompB4/44SIBikcBp8XKh+kEKCFlnAw3v5hYgBJSxomw98PkApSQMk6E/GFyAWpIHafBAojpBaghdZwGN7+YXoAqUslJsPJhBgFqST0HV2WOAGJ6AWpJPYfWsfVjwphKgFpSz6E1Nn7kD1MKUEwKOjILIOYUoJgUdGQnuSN+mFiAclLSgVn4MKsAVaWyY2ps/JgmZhCgqlR2RLZ+WEKAqlLZEckflhCgrJR2QBZALCJAWSntgOrBI36YTYDCUtzxWPmwjADlpcRDcfOLBQUoLyUeiL0fFhWgvJR4IPKHRQWoLzUehwUQywpQX2o8Dje/WFaAClPlYVj5sLAAdabWA6gyRwCxrAB1ptZX17H1Y1JYQoA6U+ura2z8yB+WEqDQFPvaLIBYS4BCU+xrO8kd8cOCApSacl+ZhQ+rCVBxqn49jY0fU8HCAlScql+LrR/WFqDiVP1a5A9rC1Byyn4lFkCsLkDJKfuV1INH/LCKAEWn8Ndh5cP6ApSe8l+cm18EEaD0lP/C7P0QRoDSU/4Lkz+EEaD21P+yLICII0Dtqf9luflFHAGqTwcsysqHQALUoD5YSJU5Aog4AtSgPlhEx9aPC8/aAtSgPlhEY+NH/hBBgCLUCEuwACKiAEWoEZZwkjvihyAClKFWWICFDyEFqEYdMa/Gxo/LTSABqlFHzMnWD5EFqEYdMSf5Q2QBylFLzMgCiNAClKOWmFE9eMQP4QQoSE0xHysfYgtQllpjFm5+kYAAZak1ZmDvhyQEKEutMQP5QxIC1KXemJ4FEGkIUJd6Y3pufpGGAJWpOyZn5UMiAtSnHpmeACINAepTj0yoyhwBRBoC1KcemUxj40f+EF2AAtUkkxFAJCZAgWqSqZy88BI/JCBAiWqTqdj5ITUBKlW3TMTNd5IToFJ1y+UaGz8uKYkIUKm65VLN37oQQKQiQKXqlkvJH1IVoFS1y4UsgEhWgFLVLheqB4/4ISkBilXDXMbKh3QFKFltM5qbXyQuQMlqm5Hs/ZC8ACWrbUaSPyQvQM3qm3EsgEhfgJrVN+O4+UX6AlStzhnFyocMBKhd/fNCVeYIINIXoHb1z4t0bP24gKQqQO3qnxdpbPzIH1IWoHg10EtYAJGTAMWrgV7iJHfED4kLUL5a6AUsfMhKgCrWSedpbPy4bGQgQBXrpHPY+iFHAapYJ51D/pCjAGWslc5gAUSWApSxVjpDPXjED9kIUMia6eOsfMhTgHLWUoPc/CJjAcpZSw2w90PWApSzlhogf8hagHrWU/0sgMhbgHrWU/3c/CJvASpaV/Wy8iFzAepab3WoMkcAkbcL6vr9D9ebzdWrX9rPPPzjr9uO+fT41MP3x0a6aQ1BbzV1bP24SORofF3/fv3cGFff9j2z2XxVPfLhtQB6icbGj/whV6ML+743UmrPbL5oP3TT/E6aq8kCiFKMLezdmuaz7UusP99sNp/82nrm58fnp65+enrsriN3jkPQXA0nuSN+yNjY0t5Gyudvd1/stne+rj9zf1j37J56/vK2EVKnQ9Bepyx8KMbICt9mS7W4eXx3XUVR5fa42tk/tT365JDGEHTZQWPjx6UhcyMrfPs6ax8ptSzqO2r7v18MDEGXVWz9UJqRFX58nXWy5GnYB9D26Jv3f9u205c/dg1Bl1XkD6UZH0CHjZ/+HeZ9TN1trv5eddSr9ksxbVaxAKI4I0u8Hjr3jV3og+0C6PnF2W2tpWqbQX+paLNn9eARPxRhzgC6rRZAu7thV9+83b13elM/VgCdsPKhPPMF0MPt/h1Ch5XQ07873pAXQHtuflGo2QLoadnTuju2e/Sm8Vjx7Wbvh2LNFUDv33Tlz9M/bB5cfLvJH4o1012wd9ebzWddb37uSKvS+80CiHLN8z6gbSZtvup877MAanHzi3LN8k7ou03fjbGu5VLhHWflQ8Gm/12wp5A5iaTavk/ththxCKX2XZU5AohyTf/b8LtXWZ+cfEziNqKqe+8Pt5v2b4UV2ncdWz9lXghKdtHnAf3c83lAjUXO0x35796efEJQfQhl9l1j40f+UKLpPhFxHzx3J/9Nf3ro3fXxgfbeUJmNZwEEl3wm9G+Nz4SuAqj++fP7AHp892ZzevDJEIpsvJPcET8Uarq/ilEFUP3z5w8B9Pjwx+7TOD795l9dQyix9Sx84NHfBVtBY+OntNOHmgDVX1YH2vqBowDVX1YHyh84ClD+RbWgBRDUBCj/olqwHjzih+IFaICSmtDKB+oCtEEhrejmF7QEaIMiWtHeD3QI0AZFtKL8gQ4B+qCEXrQAgi4B+qCEXnTzC7oE6IQCutHKBzoF6Ie8e9LNL+gXoB9y7kl7PzAkQD/k3JPyB4YEaIiMm9ICCAYFaIiMm9LNLxgUoCXybUsrHxgWoDFybM4qcwQQDArQGPk1Z8fWT3bnCFMI0Bj5NWdj40f+QI8AnZFdd1oAwZkCdEZ23XmSO+IH+gXojdz608IHzhWgRTJq08bGT0ZnBrMI0CLZtKmtH3ihAC2STZvKH3ihAD2SS59aAMFLBeiRXPq0HjziB84RoEsy6VQrH3ixAL2Sfr+6+QXjBOiV1PvV3g+MFaBXUu9X+QNjBWiWxBvWAghGC9AsiTesm18wWoB2SbtlrXxgvABNk3jjCiAYLUDTpNq4VeYIIBgtQNOk2biNjR/5AyME6Jo0O1cAweUCdE2SnXvywkv8wDgB+ibJ3rXzAxMI0D4ptrCb7zCFAO2TWAs3Nn4SGz2EEqB9kmrh5m9dCCC4QID2SaqF5Q9MKED/pNTDFkAwpQD9k1IP14NH/MClAnRQQl1s5QOTCtBHafSym18wvQB9lEIv2/uBOQTooxR6Wf7AHAI0UgLNbAEEswjQSAk0s5tfMIsArRS/na18YB4BGipyU1eZI4BgFgEaKm5Td2z9hB0rpChAQ8Vt6sbGj/yBiQXoqLBdbQEEMwvQUWG7+iR3xA9ML0BPRe1rCx+YW4DWCtjejY2fgCOELARorXDtbesHFhKgtcK1t/yBhQTorWj9bQEESwnQW9H6ux484gfmFKC7gnW4lQ8sJkCPxelzN79gWQF6LEqf2/uBpQXosSh9Ln9gaQGaLEijWwDB4gI0WZBGd/MLFhegzWK0upUPLC9As63d8FXmCCBYXIBmW7fhO7Z+AlwTKEOAZgsSQD71EBYXoNtW7XgLIFhRgG6LEkA+9RCWFqDf1ux5Cx9YU4C2W6n1Gxs/AgiWF6DtVml9Wz8QQIC2CxJAKwwCSheg79bofQsgiCBA360cQO59wWoCdN4K3W/lAyEE6L9lM8DNL4gjQP8tmQH2fiCSAP23bgAt97OBpgANuGAIWABBKAEacJ0AcvML1hegBZeLASsfiCVAIy4RBlXmCCAIJUAjzh8GHVs/Ac4bCNCICwaQTz2EUAJ04uxpYAEEQQXoxCUDyKceQiQBenHuPLDwgagCtOSMsdDY+BFAEEuAlpwtFmz9QHABWnLBAJrpBwHjBOjJuXLBAgiiC9CTCwSQe18QUoCunCkZrHwgvAC9OX0+uPkFaQjQm1Png70fSEWA3pw/gKb9/sBUAjTnxAFhAQTJCNCc8wWQm18QW4D2nDYirHwgHQGadKqgqDJHAEEyAjTpNEHRsfUT4NyAIQGadOIA8qmHkIwAXTpJUlgAQYICdOnUAeRTDyEVAfp0iqyw8IEUBWjXCyOjsfEjgCAdAdr1osiw9QMJC9CuEwfQZOMC5hagXy/JDAsgSFmAfp0ogNz7guQE6NgLUsPKB5IWoG/HZYebX5C+AH07Jjvs/UAOAvTtNAE0/biAuQVo3BHhYQEEWQjQuJcFkJtfkK4Arfvy+LDygTwEaOALV0BAsgI08EtCpMocAQRZuKCB3/9wvdlcvfrlrKcGDj4/RBobP/IHEje+g3+/fo6Aq2/PeGrgYAEExRrdwffHV0E3H31q4OAXBNDJCy/xA+kb28MfXm82n21fUP35ZrP55NePPDVw8OPYAALSN7aV7zabz9/uvnj4frP5+iNPDRz8eH4AufkOuRnZytskufrp+ct311W69D41cPDTEKyAoFAjW3n7omofJLV46Xlq4OCnIQggKNTIVr7fbL7Yf317urPcfmrg4KchjLgLBuRgfAAd9nLuWgHUeGrg4KchCCAo1MherufI/enGcvupvoP/Unn5O6GBLCQWQEBOBBCwmjUDaD8EAQSFEkDAapK6CwbkJan3AQF5Semd0EBmUvpdMCAzCf02PJCbiz4P6Of+zwP6ufV5QN0HPwogKNd0n4i4TZnqhdZcn4gIZGZ88//W+JjnYwC1nup6pDYEAQSFmu6vYtQCaK6/igHkJUDzCyAoVYDmF0BQqgDNL4CgVAGaXwBBqQI0vwCCUgVofgEEpQrQ/AIIShWg+QUQlCpA8wsgKFWA5t8AhWh1/xqR03DGsHd/O6MITjQ3TvREq/nXSJyX257c2kNYhhPNjRMdJIBicaK5caKDBFAsTjQ3TnSQAIrFifqvAJwAAAYtSURBVObGiQ4SQLE40dw40UECKBYnmhsnOkgAxeJEc+NEByUSQECOBBCwGgEErEYAAasRQMBqBBCwGgEErEYAAasRQMBqQgXQwB+Qf9Ffmw+vf+wP//jrZrP59PjUw/fHD3O6WXCI0+g90a7TynBG704/jevr3WNpz+jOh9ef/Nrx8KgejRRAv18/z8rVt2c8NXBweP1j3z+z2XxVPfLhdcLl2n+iHaeV44x2BVDSM7qzTdCuABrXo4EC6L5/XtpPDRwcXv/Ya89svmg/dNP8TsGdN6PVc1nOaFcApTyjOw+3m64AGtmjcQJo9x+Gz7aLtT/ftM6v/dTAweH1j/3pmZ8fn5+6+unpsbs0q3RnaJJap5XnjNbc7f+bkvCM7jy9gmyf5dgejRNA23n5/O3ui90Zfv2RpwYODq9/7PeHdc/uqecvb5Nrx4OhSWqdVp4zenS/PyblGd364+llVfsMxvZomADajrL6b/7ju+v9XPU9NXBweANjvz3+t3H/1PbotE7vaGiSWqeV6YwebJcD1TEJz+jj4/vtambz6k07gEb3aJgA2s7QfpC1ofc8NXBweOeNfX/U9n+/WGxo0xo60dZp5T6jt4dFQMIz+rSqufquaxN6dI+GCaDjy4+TlUD3UwMHh3fe2PfTtz365v3ftv/Z+fLHZYY3naETbZ1W5jN6fAGW8oxuA+jqq7edd8FG92ikADq8TrxrBVDjqYGDwztv7Pvpu9tc/b26k/AqsYX70Im2TivvGa0vARKe0cfHf1fbAl0BNK5HwwRQfYz3p5tW7acGDg7vrLEftgxua/dsE9s6GDrR1mnlPaN3p6uBVGe00hVAo3tUAC3trLHfVhW7u4Fw9c3b3XtKN4md59CJtk8r6xk97kCnPaMVAZR3udbf6lUr3bvU3h8zcKLt08p6RuvbISnPaEUA5V2uz/+RbN012D160z44rvMmqTqtnGe07yZQcjNaEUBZl+vTey26CvYutxM9HJb5jPa+DSa1Ga3kGUDuglW25br5rGtlnlpfnjlJz4flPKO9OZPajFbyvAvmfUDPdr+++FXnfy9TK9czJ+kQQLnOaP/b8FKb0Uqe7wPyTugnd/23RlJbGJw5Sc+nle+MDvwiQmozWsnzndB+F2znrrH9U1u91+/lJmHgRNunle2MNl+BpTyjla4ASv93wfw2/OPTsvWTk4+P205dNdcPt5vUfoeo/0Q7TivTGX3cvf6ox0zSM/qs8wPJkv9t+MOH4fR9HtDPrc8a6T44vP6xt/+T+HRH/ru3J58QlIz+E+04rTxn9LHVrknP6LPOABrbo3ECqP0Basd+zPwTEfcnevr5eU8Pvbs+PpDYumBoRjtOK8sZfTzZC3mS9Iw+qQfQxT0aKIAef2t8hGxtFptPdT2Sjp4TrX9a+T6AHt+92WR3oo+dp5XhjO60NkCSntGd7gAa2aORAqj5Ifr1VyRZ/1WM6kTrn1Z+CKDHhz92n93w6Tf/Wm+44/XPaMdp5TejO9sAauz0JD2jj70BlP5fxQAKI4CA1QggYDUCCFiNAAJWI4CA1QggYDUCCFiNAAJWI4CA1QggYDUCCFiNAAJWI4CA1QggYDUCCFiNAAJWI4CA1QggYDUCCFiNAAJWI4CY29Nfxnr4/b9tNp/9uP2/D/+43mw+/e7pqZT/IjNTEEDMbRdA/+/7/Z/ie1/9Waynv1UjgEongJjbLoD+5/6Pnf2vw19fvHkUQAgg5vb0Bxd3fyX8/dNfXvzsl8fHP66fl0ACqHQCiLntAug5W3Z/Lfzw1e4LAVQ6AcTcdgF0s/+qypvtV7s/7yuASieAmFsVNl1fCaDSCSDmJoDoJYCYmwCilwBibgKIXgKIuQkgegkg5jYQQI+3hwC62wigAgkg5jYcQM+/k/H0JkUBVB4BxNyGAmi77tl89fbx4ffrjQAqkQBibkMB9PRrGk/+x2sBVCABxNyGAujx/rr6NfkPAqhEAoi5DQbQ47//9zaCvvzxUQAVSQABqxFAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABqxFAwGoEELAaAQSsRgABq/n/MreN7OgR5HwAAAAASUVORK5CYII=" alt="Fig 1a. Probabilities against Probabilities" width="576" />
</div>
<p>The first part of the <em>logit</em> function:</p>
<ul>
<li><span class="math inline">\(\frac{\mu}{1 - \mu}\)</span></li>
</ul>
<p>unbounds <span class="math inline">\(\mu\)</span> on the right side, so that as it goes to 1,
transformed, it goes to infinity, shown graphically below</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 1b. Probabilities against right unbounded probabilities
</p>
<img role="img" aria-label="Fig 1b. Probabilities against right unbounded probabilities" src="data:image/png;base64,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" alt="Fig 1b. Probabilities against right unbounded probabilities" width="576" />
</div>
<p>The next part, the natural logarithm, unbounds it on the left side
because the log of 0 is negative infinity</p>
<ul>
<li><span class="math inline">\(ln\left(\frac{\mu}{1 - \mu}\right)\)</span></li>
</ul>
<p>Combined, the graph below shows the raw <span class="math inline">\(\mu\)</span> values against the
transformed values.</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 1c. Probabilities against unbounded probabilities (logit scale)
</p>
<img role="img" aria-label="Fig 1c. Probabilities against unbounded probabilities (logit scale)" src="data:image/png;base64,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" alt="Fig 1c. Probabilities against unbounded probabilities (logit scale)" width="576" />
</div>
<p>In this way, the link function for logistic regression takes the
probability of the event occuring, which can only fall between 0 and
1, and transforms it to fall between negative infinity and positive
infinity</p>
<p>Now we have a continuous and unbounded outcome we can apply
a linear model to!</p>
<p>To go from predictions on the linear model back to the probability
scale, we use the inverse link function:</p>
<p><span class="math display">\[ \mu = g^{-1}(\eta) = \frac{1}{1 + e^{-\eta}} \]</span></p>
<p>That is, suppose we had the linear predicted values, <span class="math inline">\(\eta\)</span> shown
below graphically</p>
<div class="figure">
<p class="caption marginnote shownote">
Fig 2a. Linear predictor against linear predictor
</p>
<img role="img" aria-label="Fig 2a. Linear predictor against linear predictor" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABIAAAAMACAMAAABrYew+AAAAulBMVEUAAAAAADoAAGYAOjoAOmYAOpAAZrYzMzM6AAA6OgA6Ojo6OmY6ZmY6ZpA6ZrY6kNtmAABmOgBmOjpmZjpmZmZmZpBmkLZmkNtmtrZmtttmtv+QOgCQZjqQZmaQkJCQtraQttuQ2/+2ZgC2Zjq2kDq2kGa2tpC2tra2ttu229u22/+2///bkDrbkGbbtmbbtpDbtrbb25Db27bb29vb2//b/7bb////tmb/25D/27b/29v//7b//9v////wx7y0AAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO3da2MbRaKg4XYSwAc2kMBsWAK7BzzLsIAHZjls7Az2//9bK8lSq9VqdXSp7ro9z5dJLMYt9eVNqUqX5hEgkib2HQDqJUBANAIERCNAQDQCBEQjQEA0AgREI0BANAIERCNAQDQCBEQjQEA0AgREI0BANDED1Kgf1E2AgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGhCNODh26b1tn/j+++um+bq5S9D2xYgqFuIBvz16nCAfrt++vnV1wPbFiCoW4gG3DUHA3Q3MjYSIKhdiAbcDtVlZTk2erF49vXH66Z59uvetgUI6haiATcDcXmySNNH75Z/WE4TfbG3bQGCugVowCIuT5UZuuXqh6c/3l/v/0cCBJlbTa9c8v+//C4snmd9fPCWTXU6LdpuW4AgZ+0M7/m/4fI7cdc0b99/ubgTn32/f0ubppv9iSIBgqwlEaDb5uqr9d14ufss664z8TMwUy1AkLPO8vfZv+Lye3HTuRu78zzd6HRj9MmaAEHGkgjQcoHr6s275Wuem95SlwBBuZokAvTXq3Z6+bb3ah8BghKtm5NEgDqWg6HuRM+hAG22LUCQn2bA2b8r5B1bFueL3b8KEBRmW50kVsE6epWxCgbFCTkAmjxAXgcEZdnpzmX5meApWLcyXgkNpQky8Nn+tot/Q2fep7MgtuK9YFCQ3sRPGgFapGW99v5w0/TeFebd8FCKkFM/21968W9YvRDxm3dPH/rTe5q1+jygn30eEORviv6EmAO6v97eo6dRzvapmE9EhDJMMgAKMgl9/3p9fzYf/NyZC/qnz4SGEnTDEyo/gVbBHn5ffhrH8zd/rv/enYz2rRhQgMAjn/bXBvxdJ29bgCB9Eyx+bX93wN918rYFCFI3zdxP+9sD/q6Tty1AkLpJ+yNAwIhpB0ACBIyYZvFr++vD/rrTti1AkLapRj7t75/ilx67bQGCZE25+LXdyBS/9NhtCxAkauK5n3YzU/zSY7ctQJCoefojQMC+mQZAAgTsm3jxa7udiX7vUdsWIEjS5COfdkOT/vYPbFuAIDWzLH5ttzbpb//AtgUI0jLX3E+7vUl/+we2LUCQlpn7I0BAa+4BkAABrbkWv7YbnHoDY9sWIEjJfCOfdovzbGZ42wIEaVg3R4CAuQ1M/QgQMI/exM98/REgqF68AZAAQfV2ujNnfgQIqhdh4LPd9twb7G5bgCCq3sSPAAFziTf1s70Lc2+wu20Bgoji90eAoFYJDIAECGrVDU+c/AgQ1CrqyKe9E9G2LEAQSfTFr+09ibZlAYIoUpj7ae9LtC0LEESRUH8ECCqT0gBIgKAyKSx+be9MzG0LEMwtjZFPe29ibjuBxw/1SGfxa3uXYm47gccPtUhq7qe9UzG3ncDjh1qk2B8BgjokOQASIKhDUotfLQGCGiQ28tkQIChcgotfLQGCoqU597MhQFC0pPsjQFC0tAdAAgRFS3PxqyVAULBURz4bAgRFWjdHgA5vO8k9AgUYmPpJ8nITIChQb+In1f4IEBQolwGQAEGBdrqTbn4ECMqSx8CnJUBQjlyeebUECMohQKdsO/F9A5nJrj8CBOUQoJO2nfrOgazshCeH/AgQFKETnSxGPhsCBNnL76nXhgBB9rLtjwBB9vIdAAkQZC+/ueeWAEHmchz5bAgQ5CvXxa+WAEGuMp772RAgyFX+/REgyFUBAyABglxlvPjVEiDIU9Yjnw0Bguxkv/jVEiDITAlzPxsCBJkpqD8CBJkpaQAkQJCZEha/WgIEWSlj5LMhQJCJdXMEKNS2C9h/MJOBqZ8CLiABgiz0Jn7K6I8AQRbKHAAJEGRhpzul5EeAIAuFDXxaAgRp6038lHXZCBCkrMypn5YAQcrK7o8AQcoKHwAJEKSsG57y8iNAkLJiRz4bAgRJKnrxqyVAkKDS5342BAgSVEl/BAgSVMsASIAgQaUvfrUECJJT/shnQ4AgJXUsfrUECNJRzdzPhgBBOmrrjwBBOqobAAkQpKOaxa+WAEEqKhr5bAgQJKCyxa+WAEF09c39bAgQRFdtfwQIoqt3ACRAEF19i18tAYLIahz5bAgQRLNujgDF2XZ1exs6BqZ+qrskBAgi6U381NgfAYJIDIAeBQhi2elOnfkRIIik6oFPS4Bgbr2Jn5ovBAGCeZn66RAgmJf+dAgQzMoAqEuAYFbd8NSeHwGCeRn57BAgmInFr30CBLMw9zNEgGAW+jNEgGAOBkCDBAjmYPFrkADBDIx8hgkQTMvi14ggO+Phx08Xu/X5y1/2b/l2u9vf7m3bkaB45n5GhdgZv11v9uzn/Zv+eiVAVE1/RgXYG3edffvxyG0CRH0MgMZdvjeWg5wXPy/+8Mfrprn6YffG24HubLftUFA6i1/jLt8fd+24Zznh0xsC3TTPfj28bQeDwhn5fMDle+VmO8i5v24+ete9bZGk3R/sbtshoVwWv44RdK8sno3t9mbxg/6sUHfbDgmlMvdznGkDtHh69vb9l4t9/9n3Q9t2SCiV/hwn6G65688B3TZXX613/8v9p2KOCaUyADpSyN2yGAD1VsFuOvu/Mzb6ZM0xoVAWv44Ucsfc9AdAy2WxqzeL8Lz/bnEIvmh/LkCUzcjnWOF2z8OiP701986Q6LZ7owBRqnVzBOhIwXbParTzw+jN/ZckOjYUZmDqx0k+KtTueT/wMugdt93nYOttOzaUpTfxoz8fFGj/3F83zYvDr3l+XK2QCRBlMwA6WZj9sxjeNJ8ffsnzkgBRvJ3uyM8xguyh22a/LgP/jTkgimbgc7oQO+r20PRPZ95n/zVCAkQ5ehM/Tu1jhfk8oGf7n4W4dH+9WXt/2HuN0KMAUQpTP2cL8nlAh5a/Vkvz37wb/qggAaIU+nO2y/fU7c6OX2WmbdL99faW/Ukih4kiGACd7+I91f3Y+b0APd6/3vz864FtO0yUoBse+TnNxfuq+7Hz+wF6fPh9+Wkcz9/8ObRtB4oCGPlcwPeCwdk6ox4BOosAwZnM/VxOgOBM+nM5AYLzGAAFIEBwHotfAQgQnMXIJwQBglNZ/ApGgOA05n4CEiA4jf4EJEBwEgOgkAQITmLxKyQBgiMZ+YQnQHAUT72mIEBwFAGaggDBMfRnEgIExxCgSQgQHGEnPPITjADBqHVtjHwmIUAwYuCZl9M2IAGCEb3nXfoTmADBYQZAExMgOGynO/ITngDBQQY+UxMgGNKb+HGyTkOAYJ+pn5kIEOzTn5kIEOwxAJqLAMGebnjkZ0oCBH1GPrMRIOiw+DUvAYKWuZ+5CRC09GduAgQbBkCzEyDYsPg1OwGCNSOf+QkQWPyKRoDA3E80AgT6E40AUT0DoHgEiOpZ/IpHgKidkU9EAkTFLH7FJkBUy9xPfAJEtfQnPgGiVgZACRAgamXxKwECRKWMfFIgQFRn3RwBSoAAUZmBqR8nYjQCRGV6Ez/6E5UAURcDoKQIEHXZ6Y78xCZAVMXAJy0CRC16Ez9OvxQIEHUw9ZMkAaIO+pMkAaIKBkBpEiCq0A2P/KRDgKiBkU+iBIjCWfxKmQBRNHM/aRMgiqY/aRMgSmYAlDgBomQWvxInQBTMyCd1AkSZLH5lQYAokbmfTAgQJdKfTAgQBTIAyoUAUSCLX7kQIMpj5JMNAaIoFr/yIkAUxNxPbgSIguhPbgSIchgAZUeAKIfFr+wIEMUw8smPAFGAdXMEKDsCRPYGpn6cWpkQILLXm/jRn4wIELkzAMqYAJG7ne7IT14EiMwZ+ORMgMhXb+LHCZUfASJXpn4KIEDkSn8KIEBkygCoBAJEprrhkZ9cCRB5MvIpggCRHYtf5RAgMmPupyQCRGb0pyQCRF4MgIoiQOTF4ldRBIisGPmURYDIhcWvAgkQeTD3UyQBIg/6UyQBIgsGQGUSILJg8atMAkQOjHwKJUAkzuJXyQSIpJn7KZsAkTT9KZsAkTIDoMIJECmz+FU4ASJhRj6lEyCStG6OABVOgEjQwNSPk6VIAkSCehM/+lMsASI9BkDVECDSs9Md+SmZAJEcA596CBAp6U38OEVKd+wB/q93E2zb2cUOUz/VOXyAH/7xt41P/6N59usE23Z2sUN/qnPwCN9d75wIAsTkDIDqc+gI3+/2p3npKRhT64ZHfupw6BjfLqPzj1fN1f/48XXTXL2dZNtOMJ4Y+dTqwJF++LZpvnh8vGmat6sYfTTBAEiAeOKpV70OHOm/FmOfH1bp+eKpRlMMgZxmrAhQvQ4HaDntfNc0Hz+2/xN8204zHvWnauMBur9ePfla/G2K52DOM5YEqGKH54CWAVqXZ52j4Nt2ntF744X8VObQwb5ZzQFtOyRAhNeJjpFPnUaW4ZfTPk/LYHcfWgZ7/91101y9/OW0m5xvdfPUi4MBWgx6ltFZpOfZz//31QcmoX9bv2rx6utTbhKgyukPI2/FWL39YrkCv+rHDyO/4257BvVX60duEqDKGQAx9mbU31+vpn9er/rzzcivWA6WXiyeYv3xeu8tYyM3PQpQ5cw9c8zHcfz+t7+9+XPsP2hfKL1++fRxNz0KUN2MfHgM8YFki7ZsnqCtXzZ0zE2rbTvx6mTxi41DrwP610//p9OLf/345uAqWOdVip3gfOim1badeDUy98PW+CuhB//W032fxs3uXPPITattO/FqpD9sBQlQO7tzuxegQzettu3Mq5ABEB37B/+fyw9h/eq6ufpv7UeyDq5hbXTLcrc71Xzopk/WnHkVsvhFx/7h738W4pPDL0QUIE5g5EPXwElwM9CfF4ffCiZAHGXdHAGiY+AkePjpp5/+sXgK9p8/tf5r5DecEaDNtp2B9RgaVse+T8R31CT0KAHiCL2JH/1h5bjXAY2xCsaHGQAx6PKzwOuA+LCd7sgPG6Pnwb9/Wo6DHkbfCeaV0HyYgQ/DRk6H3/6jWb3+569XL4Y+TmzDe8EY05v4cdDpOnw6/H11tqwCNP5xQN4Nz0Gmfhh18HRYfjXqi/91vf5QsrFPZF196M/Phz8PaPimRwGqgf4wauy74b9ZBGSZjQ99MeHexx5ux0w+EbFuBkCMO/ytGMsFrKcAffCLCf/Z++DnzpO2/k0723Yylq4bHvlh3+HvBVsmZB2goRnkHb2vvujOGvlWjIoZ+fAB46+EXgfI94JxKotfHEOAmIC5H44T5inYmdt2UpZKfzjOyCT0F22Abj8wCX3utp2VhTIA4kiHToy79WsQlwG6G1xED7BtZ2WhLH5xpEOnxvK1P1ffLwP08L+bD301/Lnbdl6WyciHYx08QZYvYm6NvhXj/G07O4tj8YuTHD5BNl8L3zx9u/IU23Z2FsbcDycaO0Hef7d8P/zVy5+n2razszD6w4liniFOz8IYAHEqASIYi1+cSoAIxciHkwkQAVj84jwCxMXM/XAuAeJi+sO5BIhLGQBxNgHiUha/OJsAcSEjH84nQJxt3RwB4mwCxJkGpn4cUE4kQJypN/GjP5xBgDiPARABCBDn2emO/HAeAeIsBj6EIECcqjfx4zByPgHiNKZ+CEiAOI3+EJAAcRIDIEISIE7SDY/8cCkB4hRGPgQlQBzJ4hfhCRBHMffDFASIo+gPUxAgjmEAxCQEiGNY/GISAsQRjHyYhgAxzuIXExIgxpj7YVICxBj9YVICxAgDIKYlQIyw+MW0BIjDjHyYmAAxyOIXcxAgBpj7YR4CxAD9YR4CxD4DIGYiQOyz+MVMBIg9Rj7MRYDoWDdHgJiJANEamPpxiJiUANHqTfzoD5MTIDYMgJidALGx0x35YQ4CxJqBD/MTILzxi2gECFM/RCNA6A/RCFD1DICIR4Cq1w2P/DAvAaqdkQ8RCVDFLH4RmwBVy9wP8QlQtfSH+ASoVgZAJECAamXxiwQIUKWMfEiBANXH4hfJEKDamPshIQJUG/0hIQJUGQMgUiJAlbH4RUoEqBpGPqRHgCrhqRcpEqBKCBApEqA66A9JEqA6CBBJEqAq7IRHfkiGABVuXRsjH5IkQEUbeOZlp5MQASpa73mX/pAYASqZARCJE6CS7XRHfkiPABXMwIfUCVCZehM/djVpEqASmfohEwJUIv0hEwJUIAMgciFABeqGR35ImQCVx8iHbAhQUSx+kRcBKoi5H3IjQAXRH3IjQOUwACI7AlQOi19kR4CKYeRDfgSoBBa/yJQA5c/cD9kSoPzpD9kSoOwZAJEvAcqexS/yJUC5M/IhYwKUMYtf5E6AsmXuh/wJULb0h/wJUK4MgCiAAOXK4hcFEKBMGflQAgHKzro5AkQBBCgzA1M/diPZEqDM9CZ+9IesCVBeDIAoigDlZac78kPuBCgrBj6URYBy0Zv4sfMogQDlwdQPRRKgPOgPRRKgLBgAUSYBykI3PPJDOQQoB0Y+FEqAEmfxi5IJUNLM/VA2AUqa/lA2AUqZARCFE6CUWfyicAKUMCMfSidAabL4RRWCnNgPP366uESev/xl/5Zvt5fQ271tu6oOMPdDJUKc2L9db66Sz/s3/fVKgM6gP1QiwJl917lOPh65TYCOZQBELS4/s5eDnBc/L/7wx+umufph98bbge5st+2yGmbxi1pcfm7fteOe5YRPbwh00zz79fC2XViDjHyoxuVn+M12kHN/3Xz0rnvbIkm7P9jdtsurz+IXdQl6hi+eje32ZvGD/qxQd9sur13mfqjNtAFaPD17+/7LxXX02fdD23Z57dIfahP0FL/rzwHdNldfrS+ll/tPxVxfuwyAqE7IU3wxAOqtgt10rqXO2OiTNdfXDotfVCfkSX7THwAtl8Wu3izC8/67xeX0RftzARpi5EN9wp3qD4v+9NbcO0Oi2+6NAtRj8YtKBTvVV6OdH0Zv7r8k0XX2xNwP1TrvVG/f4tUm5/3Ay6B33Hafg6237Tpb0R+qFShA99dN8+Lwa54fVytkAjTIAIh6hQnQYnjTfH74Jc9LAnSIxS/qFeRsv2326zLw35gDGmLkQ8VCnPO3h6Z/OvM++68REqB1cwSIeoX5PKBn+5+FuHR/vVl7f9h7jdBj7QEamPqpen9QpSCfB3Ro+Wu1NP/Nu+GPChKgnYkf/aFGl5/0tzv/hq8y0zbp/np7y/4kUdVXnAEQBAhQ92Pn9wL0eP968/OvB7Zd8xW30x35oVIXn/bdj53fD9Djw+/LT+N4/ubPoW1XfM0Z+MCj7wWLoDfxU+legCUBmpmpH9gSoJnpD2wJ0LwMgKBDgObVDY/8UD0BmpWRD3QJ0FwsfsEeAZqHuR8YIEDz0B8YIECzMACCIQI0C4tfMESA5mDkA4MEaGIWv+AwAZqUuR8YI0CT0h8YI0BTMgCCUQI0JYtfMEqAJmTkA+MEaBoWv+AIAjQFcz9wFAGagv7AUQRoAgZAcBwBmoDFLziOAIVn5ANHEqCQ1s0RIDiOAIUzMPVT2COEwAQonN7Ej/7AhwhQMAZAcCoBCmanO/IDRxCgAAx84DwCdDHPvOBcAnQxAYJzCdCl9AfOJkCXEiA4mwBdaCc88gMnEaDzdaJj5APnEKBzeeoFFxOgc+kPXEyAzmQABJcToDOZe4bLCdB5jHwgAAE6mcUvCEWATmTuB8IRoBPpD4QjQKcxAIKABOg0Fr8gIAE6iZEPhCRAx7L4BcEJ0HHM/cAEBOg4+gMTEKCjGADBFAToKBa/YAoCdAwjH5iEAI1bN0eAYAoCNGZg6if5+wwZEaAxvYkf/YGwBGiEARBMS4BG7HRHfiA4ATrMwAcmJkCDehM/Cd9TyJkADTD1A/MQoAH6A/MQoH0GQDATAdrXDY/8wIQEaI+RD8xFgLosfsGsBGjL3A/MTIC29AdmJkAtAyCYmwC1LH7B3ARow8gHZidAjxa/IBYBMvcD0QiQxS+IRoAMgCAaAbL4BdFUHyAjH4in5gBZ/ILI6g2QuR+IToD0B6KpNkAGQBCfAFn8gmhqDZCRDySgvgCtmyNAEF9tARqY+hEgiKXaAD3qD0RXWYAMgCAl9Qbo0eIXxFZXgAx8ICnVBKg38SNAkIBKAmTqB1JUbYBm2zRwUB0BMgCCJFUXIGtfkI4qAmTkA2kqPUAWvyBhZQfI3A8krbYATb1F4ARFB8gACNJWS4AsfkGCSg6QkQ8krtAAWfyCHBQZIHM/kIdKAjTRhoCLlBggAyDIROEBsvgFKSswQEY+kIuyAmTxC7JSUoDM/UBmyg5Q2N8PBFZQgAyAIDdlBsjiF2ShnAAZ+UB2SgjQujkCBLnJP0ADUz8CBHkoKECP+gOZyT5ABkCQr5IC9GjxC/KSe4AMfCBjGQeoN/EjQJCdbANk6gfyV1CAgt0vYCa5BsgACApQQICsfUGuMg2QkQ+UIL8AWfyCYoS4fB++3dbgbf/G999dN83Vy1+Gtn3Gxs39QEFCXL5/vTocoN+un35+9fXAtoME6Ky7DKQgxPV71xwM0N3BWx7PCpABEJQkxPV7O1SXleXY6MXi2dcfr5vm2a97274oQBa/IHshruCbgbg8WaTpo3fLPyynib7Y2/bJGzfygaIEuI4XcXmqzNAtVz88/fH+ev8/OikiFr+gPAGu48XzrI8P3rKpTqdF220fv3FzP1CiANfxXdO8ff/lIgmffb9/S5umm/2JoosCdMEdBhIR4EK+ba6+Wlfh5e6zrLvOxM/ATPXxFTEAgiIFuJBvOlnYnefpRqcbo0/WzgmQxS8ox+WX8nKB6+rNu+VrnpveUleoABn5QJkuv6D/etVOL9/2Xu0zyQgIKEbQC3o5GOpO9BwK0GbbAgR1O++Cbt/91Vtav92tTLAA+covKFLYAPUqE2wVTICgSFMHKNDrgHzlF5Qo7DXdG+aEeyU0UKLLG9CZ9+ksiK2EfC8YUJ7LG7BIy3rt/eGm6b0rLPS74YGiBHoh4jfvnj70p/c0a/V5QD8H/DwgoCQBGnB/vX2VztMoZ/tULPQnIgIlCdGA+9ebNbH1Bz935oL+GfgzoYGCBGnAw+/LT+N4/ubP9d+7k9GBvxUDKEh+3wsGFEOAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIgmboCAquxFIEZ52o2fYvld8uXzKMvhUQ7Ya0CM8Jxl8UBj34UZeJTl8CiPIEBp8SjL4VEeQYDS4lGWw6M8ggClxaMsh0d5BAFKi0dZDo/yCAKUFo+yHB7lEQQoLR5lOTzKI+QTIKA4AgREI0BANAIERCNAQDQCBEQjQEA0AgREI0BANEkH6OHb7QcZve3f+P6766a5evlLjDsW1sOPny4e4POBhzK6A/IxcqgcxayEvyKTDtBfrw4/3N+un35+9XWUuxbQ5pE0zef9m8Z2QD5GDpWjmJfwV2TSAbprDj7cu2KOafdBfjxyW7YPc+RQOYqZCX9FJh2g24OPZVniF4ux3h+vm+bZr/Peq7BWj+Tnx6eHcvXD7o2Hd0A+Rg6Vo5ib8Fdk0gG6OfhQFjvio3fLPyyflH4x530K7a79F3P5UHr/eB7eAfkYOVSOYm7CX5EpB2jxUJ4e09Atm39m7q8P/Ud5uNn+m7L3UA7vgHyMHCpHMTcTXJEpB2gxqus/nd7esnmMnUeeu86jan9wYAfkY+RQOYq5meCKTDlAi3Ht2/dfNk3z2ff7t7Q74qaYZ9h7p+7hHZCPkUPlKOZmgisy5QDdNldfrefVX+6O6e46TzPLmeK7688eHN4B+Rg5VI5ibia4IlMO0E1nzW/3H5XuQ7zLfP6ytfinszd0PbwD8jFyqBzF3ExwRSYcoOV0+tWbd8tXWDa9h1TkqXvT/6dzZAfko7YAlXkUn0xxRSYcoM6/Jbe91xYUeOo+3Ay9TObQDshHXQEq9Sg+meKKTDhAHcv0dp9Wlnfqrv5xObx20N8B+agqQMUexT3BrsjEAtS+16R3GG+LOnX3H+X7gRfQ7rjN71E+qSlA5R7FfaGuyEwC1HtMma+f7D3K++umeTE6OM/2Aq1oFazgo7gv1BWZbYByfgVJ/1Eujljz+fj6SLanbj2vAyr5KO4LdUUmFqBDelEt6zW0t0esjmQ7QqjmldBFH8V9oa7IhAPUeZbZf3FFQe8iWj3O4QM2sgPyUcd7wUo/ik+muCITDtDigaxX+h72XlxRzvuol4PXZ8MfIje2A/JRxbvhiz+KK1NckQkHaLWm+c27wc9Y2Xz+ShGfJHPoX8WxHZCPkUPlKOZliisy4QCtVhU2npq6Pc7FfJbebdO1enTto9zfATnaO1SOYq4muCJTDtDj/evNEV1/zGznH5p/lvFpwt1P+d47dfd3QJb6h8pRzFb4KzLpAD0+/L587//zN3+u/94d6ZbxfQrdT/neP3X3dkCeeofKUcxX8Csy7QABRRMgIBoBAqIRICAaAQKiESAgGgECohEgIBoBAqIRICAaAQKiESAgGgECohEgIBoBAqIRIOb3/vvY94BECBBze/h77h9NSjACxNwK+no+LiVAzE2AaAkQcxMgWgLE3ASIlgAxuYffPm2a5rPvV9+cufn+qNWXR/37x+UtV59ZFauVADG19uvsXiy/saUboO33+WX+zfCcS4CYWOfrNJff2dsJUPf7RD0pq5MAMa3Vl4Z/v3wetgjRx8ufbOaAlrd8vvyGu+X3iRsC1UmAmNZdG5fNt2huAnS3DtJqkLQcHFEfAWJaN9vv7l2XZ38VbJEmAaqTADGpRVvaZ1eLgc5yyNML0L//9T+vGwGqlAAxqeVET8cyRtsAPfz+5XVnfpr6CBCT6qyB7QWoe5sA1UmAmNQiMv0Fru4qWNM8/+y//+f/MwdUKwFiUgPzy5sA3a5fmmgSumICxKQevl2/62JrHaDFLZv1sTtPwWolQExrMc559kv7x84y/DZA718JUK0EiGktZ3quvnn3+PjvvzftCxFX00I3T0/BHnnZNK0AAAChSURBVH5czkW3LxaiKgLExO46i2CruZ+nxa+3OzcIUKUEiKndXe/0ZzUttPrz3zfxebM/UUQdBIjJPaw+9ef5mz83f/9u8dfPF3/4/cvVz9913hZGXQQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIhGgIBoBAiIRoCAaAQIiEaAgGgECIjm/wP2vkLSUp9M/QAAAABJRU5ErkJggg==" alt="Fig 2a. Linear predictor against linear predictor" width="576" />
</div>
<p>Using the inverse link function, we transform them to again fall
between 0 and 1, like probabilities.</p>
<div class="figure">
<p class="caption marginnote shownote">
Figure 2b. Linear predictor (logit scale) against probabilities
</p>
<img role="img" aria-label="Figure 2b. Linear predictor (logit scale) against probabilities" src="data:image/png;base64,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" alt="Figure 2b. Linear predictor (logit scale) against probabilities" width="576" />
</div>
<div id="logistic-regression-assumptions" class="section level2" number="4.1">
<h2><span class="header-section-number">4.1</span> Logistic Regression Assumptions</h2>
<p>Much like a normal distribution was assumed for normal linear
regression, for logistic regression a Bernoulli distribution is
assumed.</p>
<p><span class="math display">\[ y \sim Bern(\mu) \]</span></p>
<p>The Bernoulli only has the one parameter, the probability of the event
occuring.</p>
<p>In logistic regression the outcome is either 0 or 1, so outliers on
the outcome are not a concern</p>
<p>Outliers on predictors may still be a concern</p>
<p>One problem that sometimes arises is known as separation, this occurs
when some predictor perfectly predicts the outcome or separates the
outcome, most often when the outcome is rare or the sample size is
small.</p>
<ul>
<li>In a sample of 60 people where only 10 have major depression, if 80%
of the sample also have PTSD, it may happen that all cases of major
depression occurred in people with PTSD, so the percentage of
depression in those without PTSD is exactly 0%, which is
separation.</li>
<li>The usual solution is to remove predictors or collapse groups in
these cases</li>
</ul>
<p>Logistic regression still requires that the errors be independent
(i.e., individuals are independent, not dependent or repeated
measures).</p>
<p>Logistic regression also assumes that on the link scale (logit scale)
there is a linear relationship.</p>
<p>Finally, logistic regression generally requires a large sample size.
There are no degrees of freedom, requires large enough sample that
parameters are distributed about normally (central limit theorem).</p>
</div>
<div id="logistic-regression-in-r-part-1" class="section level2" number="4.2">
<h2><span class="header-section-number">4.2</span> Logistic Regression in <code>R</code> Part 1</h2>
<p>For logistic regression in <code>R</code>, we will use the <code>StressHigh</code>
categorical variable we created based off stress scores in the
baseline data collection exercise data.</p>
<p>First, let’s take a look at some basic descriptives on a few variables
we will work with. The <code>egltable()</code> function calculates basic
descriptive estimates optionally by group levels in a table.
The first argument is a list of variable names and then we give it a
dataset. The argument <code>strict=FALSE</code> is used to indicate that if a
variable has few levels, like <code>StressHigh</code> which is only 0 and 1, even
though <code>R</code> stores it as a continuous variable, it should be treated as
categorical for the table, otherwise <code>egltable()</code> will report means
instead of frequencies unless the variable is a string or factor
variable.</p>
<pre class="r"><code>egltable(
c("StressHigh", "stress", "SelfesteemHigh", "selfesteem"),
data = db, strict=FALSE)</code></pre>
<pre><code>## M (SD)/N (%)
## <char> <char>
## 1: StressHigh
## 2: 0 55 (38.7%)
## 3: 1 87 (61.3%)
## 4: stress 10.27 (2.58)
## 5: SelfesteemHigh
## 6: 0 70 (49.3%)
## 7: 1 72 (50.7%)
## 8: selfesteem 3.51 (0.77)</code></pre>
<p>Now let’s look at a cross tabulation of high stress and high self
esteem, which we do by specifying a grouping variable as
<code>StressHigh</code>. The columns of the table are now levels of Stress.
We get frequencies and percentages for <code>SelfesteemHigh</code> and means
and standard deviations for <code>stress</code> and <code>selfesteem</code> along with a
chi-squared test and t-test and effect sizes. The chi-square test is
significant, p < .001 indicating that high/low self esteem and
high/low stress are not independent. We can also see that there is
some data in all cells of the high/low self esteem and stress, although
only 11 people reported both low self esteem and low stress.</p>
<pre class="r"><code>egltable(
c("stress", "SelfesteemHigh", "selfesteem"),
g = "StressHigh",
data = db, strict=FALSE)</code></pre>
<pre><code>## 0 M (SD)/N (%) 1 M (SD)/N (%)
## <char> <char> <char>
## 1: stress 7.82 (1.43) 11.83 (1.82)
## 2: SelfesteemHigh
## 3: 0 11 (20.0%) 59 (67.8%)
## 4: 1 44 (80.0%) 28 (32.2%)
## 5: selfesteem 3.98 (0.53) 3.22 (0.75)
## Test
## <char>
## 1: t(df=140) = -13.86, p < .001, d = 2.39
## 2: Chi-square = 30.82, df = 1, p < .001, Phi = 0.47
## 3:
## 4:
## 5: t(df=140) = 6.58, p < .001, d = 1.13</code></pre>
<p>As with poisson regression, we can fit a logistic regression using the
<code>glm()</code> function. We use the usual regression formula approach,
specify the dataset and set <code>family = binomial()</code>, which gives us a
logistic regression.</p>
<pre class="r"><code>mlog <- glm(StressHigh ~ SelfesteemHigh, data = db, family = binomial())
summary(mlog)</code></pre>
<pre><code>##
## Call:
## glm(formula = StressHigh ~ SelfesteemHigh, family = binomial(),
## data = db)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.680 0.328 5.11 3.1e-07 ***
## SelfesteemHigh -2.132 0.408 -5.23 1.7e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 189.58 on 141 degrees of freedom
## Residual deviance: 157.11 on 140 degrees of freedom
## AIC: 161.1
##
## Number of Fisher Scoring iterations: 4</code></pre>
<p>The output from <code>summary(mlog)</code> is fairly similar to what we would see
for a linear regression in <code>R</code>.</p>
<ul>
<li>Deviance Residuals: these still represent model residuals, but they
are no longer raw residuals defined as <span class="math inline">\(y - \hat{y}\)</span>. Deviance
residuals are how much each data point contributed to the residual
deviance, a sort of measure of overall model fit. They are analogous
to residuals in linear regression, in that when you sum and square
these residuals, you get the sums of squares used to assess model
fit. They differ in that they are not calculated as the raw
difference between each data point and the predicted value.</li>
<li>Coefficients: the coefficients table is interpreted nearly
identically as in linear regression. The estimates are the
regression coefficients, the standard errors are given next. Instead
of t values, z values are presented because in general for GLMs we
cannot calculate degrees of freedom so we rely on the central limit
theory, and so instead of a t-test, we use a z-test (recall from
early stats that with an infinite sample size, the t-distribution
becomes identical to the normal distribution and thus the t-test and
z-test are the same, with an infinite sample and they are
functionally the same with a relatively large sample). P values are
in the final column, now based of the z-test instead of the t-tests
used in linear regression.</li>
<li>There is no model <span class="math inline">\(R^2\)</span> as that only works clearly for linear
regression. Instead, we get null and residual deviance values and an
AIC, which stands for the Akaike Information Criterion, a relative
measure of model fit taking into account model complexity. We’ll
learn more about this much later in the semester, for now you don’t
need to worry about them.</li>
<li>The number of Fisher scoring iterations. This is included because
unlike linear regression where we can directly calculate the best
parameter estimates. For other GLMs, the computer tries different
values and finds the best values, in a process known as
optimization. At each step of the optimization it evaluates how well
the specific parameter estimates work and based on some criteria
whether to keep trying for better estimates or stop trying. Each one
of these steps is called an “iteration” and the number of iterations
can give a rough sense of how hard it was for the computer to find
the values. Again you can mostly ignore these for now, although it
will become more important as we talk about mixed effects models.</li>
</ul>
<div id="logistic-regression-interpretation" class="section level3" number="4.2.1">
<h3><span class="header-section-number">4.2.1</span> Logistic Regression Interpretation</h3>
<p>At one level, we can interpret the coefficients for logistic
regression nearly identically to those for linear regression, as long
as we use the logit scale. An example follows.</p>
<p>A logistic regression predicting high stress from selfesteem (high /
low) showed that students who had low selfesteem were expected to have
1.68 log odds of being
high stress,
p < .001.
Being in the high versus low selfesteem group was associated with
-2.13 lower log odds
of being high stress,
p < .001.
A graph of these results follows.</p>
<pre class="r"><code>visreg(mlog, xvar = "SelfesteemHigh", partial = FALSE, rug = FALSE, gg = TRUE) +
ylab("predicted log odds of high stress") +
theme_pubr()</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="576" /></p>
<p>By specifying that we are working on the log odds (logit) scale, we
can interpret the results as we did before and graph the results
almost the same as before, other than needing to mention the log
odds. Although these interpretations are technically accurate, for
most people, it is hard to understand results on a log odds scale.</p>
<p>If we exponentiate the regression coefficients, specifically the
slopes, we get what are called <strong>Odds Ratios</strong> or ORs.
ORs indicate how many more times the odds of occurring the outcome will
be for a one unit change in the predictor. For example, if the <span class="math inline">\(OR = 2\)</span> and the base
odds was 0.5, then one unit higher would be <span class="math inline">\(0.5 * 2 = 1\)</span> odds. If the base
odds was 2, then a one unit higher would be <span class="math inline">\(2 * 2 = 4\)</span> odds.
ORs are interpreted as for each one unit higher predictor score,
there are OR times the odds of the outcome. Because ORs are
multiplicative, an OR of 1 means that a one unit change in the
predictor is associated with 1 times the odds of the outcome,
that is no change. Thus on the OR scale, a coefficient of 1 is
equivalent to a coefficient of 0 on the link (log odds) scale.</p>
<p>Note that although we can exponentiate coefficients, confidence
intervals, or predictions, we should <em>not</em> exponentiate standard
errors, z values or p values. To get the ORs in <code>R</code>, we can extract
the coefficients from the model using the <code>coef()</code> function and then
exponentiate using the <code>exp()</code> function and we follow a nearly
identical process for the confidence intervals.</p>
<pre class="r"><code>exp(coef(mlog))</code></pre>
<pre><code>## (Intercept) SelfesteemHigh
## 5.364 0.119</code></pre>
<pre class="r"><code>exp(confint(mlog))</code></pre>
<pre><code>## Waiting for profiling to be done...</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) 2.9369 10.780
## SelfesteemHigh 0.0513 0.256</code></pre>
<p>We can interpret logistic regression using the ORs as follows.</p>
<p>A logistic regression predicting high stress from selfesteem (high /
low) showed that students who had low selfesteem were expected to have
5.36 odds of being
high stress,
[95% CI 2.94 - 10.78].
Being in the high vs low self esteem group was associated with
0.12 times the
odds of being high stress,
[95% CI 0.05 - 0.26],
p < .001.
A graph of these results follows.</p>
<pre class="r"><code>visreg(mlog, xvar = "SelfesteemHigh", scale = "response",
partial = FALSE, rug = FALSE, gg = TRUE) +
ylab("predicted probability of being high stress") +
theme_pubr()</code></pre>
<p><img role="img" 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" width="576" /></p>
<p>Note that when calling <code>visreg()</code>, we added the new argument, <code>scale = "response"</code>. This tells <code>R</code> that we do not want the results on the
linear link scale, we want them on the original response scale. This
argument for <code>visreg()</code> is helpful any time you are working with non
linear link functions. The figure also shows how although on the link
scale there was a perfectly linear model prediction, the linear model
on the original response scale is clearly not linear.</p>
<p>Logistic regression with multiple predictors follows the same
interpretation, but just as with linear regression you need to specify
that what is being evaluated is the unique / independent association
of each predictor with the outcome, independent of other variables in
the model.</p>
<p>In addition to the odds ratio (OR) scale, with a simple model, we can
easily convert from the logit scale to the probability scale, which
may be even easier to interpret.</p>
<p>People with lower self esteem are the reference group, captured by the intercept</p>
<p><span class="math display">\[ \frac{1}{1 + e^{- (1.68)}} = 0.843 \]</span></p>
<p>People with lower self esteem have a
0.843 probability of being high stress</p>
<p>The coefficient for self esteem, indicates that people with high self
esteem have -2.132 higher log odds (the logit scale) of
being high stress than do people with low self esteem.</p>
<p>To calculate the probability that people with high self esteem will be
high stress:</p>
<p><span class="math display">\[ \frac{1}{1 + e^{- (1.68 + -2.132)}} = 0.389 \]</span></p>
<p>People with high self esteem have a
0.389 probability of being high
stress</p>
<p>Stated on the the odds scale.</p>
<ul>
<li>People with high self esteem have
<span class="math inline">\(e^{-2.132} = 0.119\)</span>
times the odds of being high stress as do people with low self
esteem</li>
<li>This is called the odds ratio (OR)</li>
</ul>
<p>An example summary of this analysis is:
“People with high self esteem were less likely to be high stress than
people with low self esteem, (OR = 0.119, p
< .001).”</p>
<p>Another way of saying the same thing:
“People with high self esteem had 0.119 times the
odds of being high stress as people with low self esteem (p < .001).”</p>
</div>
</div>
<div id="logistic-regression-in-r-part-2" class="section level2" number="4.3">
<h2><span class="header-section-number">4.3</span> Logistic Regression in <code>R</code> Part 2</h2>
<p>Next we examine a continuous predictor, continuous self esteem.
The analysis in <code>R</code> is basically the same as the previous example:</p>
<pre class="r"><code>mlog2 <- glm(StressHigh ~ selfesteem, data = db, family = binomial())
summary(mlog2)</code></pre>
<pre><code>##
## Call:
## glm(formula = StressHigh ~ selfesteem, family = binomial(), data = db)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.657 1.508 5.08 3.9e-07 ***
## selfesteem -1.974 0.399 -4.95 7.4e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 189.58 on 141 degrees of freedom
## Residual deviance: 148.48 on 140 degrees of freedom
## AIC: 152.5
##
## Number of Fisher Scoring iterations: 5</code></pre>
<pre class="r"><code>exp(coef(mlog2))</code></pre>
<pre><code>## (Intercept) selfesteem
## 2115.195 0.139</code></pre>
<pre class="r"><code>exp(confint(mlog2))</code></pre>
<pre><code>## Waiting for profiling to be done...</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) 144.5767 5.56e+04
## selfesteem 0.0588 2.84e-01</code></pre>
<ul>
<li>The coefficient for self esteem indicates that for each one unit higher
self esteem, people have -1.974 lower log
odds of being high stress</li>
<li>In odds ratios:
<ul>
<li>For each additional unit of self esteem, participants have
0.139 times the odds of being high stress (p <
.001).</li>
</ul></li>
<li>One challenge with the odds ratio metric is that it is multiplicative
<ul>
<li>If the baseline odds are 2, then 1.2 times the odds would be
2.4 (an absolute difference of 0.4)</li>
<li>If the baseline odds are 4, then 1.2 times the odds would be 4.8
(an absolute difference of 0.8)</li>
</ul></li>
<li>Important to keep this interpretation in mind, odds ratios do not
directly indicate the probability of the event occurring, just how
many times higher the odds</li>
</ul>
<p>We can calculate the specific probability of being high stress as we
did for categorical self esteem</p>
<p>Probability of being high stress for participants with 0 self esteem</p>
<p><span class="math display">\[\frac{1}{1 + e^{- (7.657)}} = 1\]</span></p>
<p>Participants with 0 self esteem have a
1 probability of being high stress.</p>
<p>To calculate the probability of being high stress for participants with a 4.5 score on
self esteem, we first calculate the log odds:</p>
<p><span class="math display">\[7.657 + -1.974 * 4.5 = -1.224\]</span></p>
<p>Then we convert the log odds to probabilities:</p>
<p><span class="math display">\[\frac{1}{1 + e^{- (-1.224)}} = 0.227\]</span></p>
<p>Participants with a score of 4.5 on self esteem have a
0.227
probability of being high stress. This matches what we can see
visually when we use <code>visreg()</code> to plot on the probability scale.</p>
<pre class="r"><code>visreg(mlog2, xvar = "selfesteem", scale = "response",
partial = FALSE, rug = FALSE, gg = TRUE) +
ylab("predicted probability of being high stress") +
theme_pubr()</code></pre>
<div class="figure">
<p class="caption marginnote shownote">
Probability of being high stress by self esteem level with 95% confidence intervals
</p>
<img role="img" aria-label="Probability of being high stress by self esteem level with 95% confidence intervals" src="data:image/png;base64,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" alt="Probability of being high stress by self esteem level with 95% confidence intervals" width="576" />
</div>
<p>Although logistic regression models do not have <span class="math inline">\(R^2\)</span> values, there
are some fit indices. For example, we could calculate the predicted
probabilities for each person and if they are >= .50, classify them as
the model predicting high stress and if < .50 classify them as the
model predicting low stress. Then we can compare the model predictions
to the observed data to calculate the model accuracy.</p>
<pre class="r"><code>accdata <- data.table(
Observed = db$StressHigh,
Predicted = as.integer(predict(mlog2, type = "response") >= .50))
## quick view of the data
head(accdata)</code></pre>
<pre><code>## Observed Predicted
## <int> <int>
## 1: 1 1
## 2: 1 1
## 3: 0 1
## 4: 0 0
## 5: 1 1
## 6: 1 1</code></pre>
<pre class="r"><code>## simple frequencies table
xtabs(~ Observed + Predicted, data = accdata)</code></pre>
<pre><code>## Predicted
## Observed 0 1
## 0 40 15
## 1 20 67</code></pre>
<pre class="r"><code>## accuracy is the average number of times predictions match observed
mean(accdata$Observed == accdata$Predicted)</code></pre>
<pre><code>## [1] 0.754</code></pre>
<div id="average-marginal-effects" class="section level3" number="4.3.1">
<h3><span class="header-section-number">4.3.1</span> Average Marginal Effects</h3>
<p>Because the probability scale is easier to interpret than is even the
odds ratio scale, people often desire to convert results from logistic
regression into probabilities. A challenge on the probability scale is
that the results are not linear. For example if looking at the graph
of continuous self esteem predicting the probability of being high
stress, the probability changes much less when moving from a self
esteem score of 1 to 2 than from 3 to 4.</p>
<p>We can see this in practice by using the <code>predict()</code> function to
generate some predicted probabilities. We make a small new dataset
with some particular self esteem values (1, 2, 3, 4) and specify the
argument <code>type = "response"</code> to get probabilities rather than
predicted log odds.</p>
<pre class="r"><code>newdata <- data.table(
selfesteem = c(1, 2, 3, 4))