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<pre><code>## (C) (cc by-sa) Wouter van Atteveldt & Jan Kleinnijenhuis, file generated June 06 2014
</code></pre>
<h1>Multilevel Modeling with R</h1>
<pre><code>*Caveat* I am not an expert on multilevel modelling. Please take this document as a source of inspiration rather than as a definitive set of answers.
</code></pre>
<p>This document gives an overview of two commonly used packages for multi-level modelling in R (also called 'mixed models' or 'random effects models'). </p>
<p>Since the yearly time series data we used so far are not suitable for multilevel analysis,
let's take the textbook data of Joop Hox on popularity of pupils in schools:
(see also <a href="http://www.ats.ucla.edu/stat/examples/ma_hox/">http://www.ats.ucla.edu/stat/examples/ma_hox/</a>)</p>
<pre><code class="r">library(foreign)
popdata<-read.dta("http://www.ats.ucla.edu/stat/stata/examples/mlm_ma_hox/popular.dta")
head(popdata)
</code></pre>
<pre><code>## pupil school popular sex texp const teachpop
## 1 1 1 8 girl 24 1 7
## 2 2 1 7 boy 24 1 7
## 3 3 1 7 girl 24 1 6
## 4 4 1 9 girl 24 1 6
## 5 5 1 8 girl 24 1 7
## 6 6 1 7 boy 24 1 7
</code></pre>
<p>Now, we can model a time series model with only the random intercept at the school level:</p>
<pre><code class="r">library(nlme)
m = lme(popular ~ sex + texp, random=~1|school, popdata)
summary(m)
</code></pre>
<pre><code>## Linear mixed-effects model fit by REML
## Data: popdata
## AIC BIC logLik
## 4454 4482 -2222
##
## Random effects:
## Formula: ~1 | school
## (Intercept) Residual
## StdDev: 0.6971 0.6782
##
## Fixed effects: popular ~ sex + texp
## Value Std.Error DF t-value p-value
## (Intercept) 3.561 0.17148 1899 20.765 0
## sexgirl 0.845 0.03095 1899 27.291 0
## texp 0.093 0.01085 98 8.609 0
## Correlation:
## (Intr) sexgrl
## sexgirl -0.088
## texp -0.905 0.000
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.35852 -0.67970 0.02436 0.59332 3.78515
##
## Number of Observations: 2000
## Number of Groups: 100
</code></pre>
<p>So, popularity of a course is determined by both gender and teacher experience.
Let's try a varying slopes model, with teacher experience also differing per school,
and see whether that is a significant improvement:</p>
<pre><code class="r">m2 = lme(popular ~ sex + texp, random=~texp|school, popdata)
anova(m, m2)
</code></pre>
<pre><code>## Model df AIC BIC logLik Test L.Ratio p-value
## m 1 5 4454 4482 -2222
## m2 2 7 4456 4496 -2221 1 vs 2 1.915 0.3838
</code></pre>
<p>So, although the log likelihood of m2 is slightly better, it also uses more degrees of freedom and the BIC is higher,
indicating a worse model. The <code>anova</code> output means that this change is not significant. </p>
<p>Next, let's have a look at the slope of the gender effect.
First, a useful tool can be a visual inspection of the slope for a random sample of schools, just to get an idea of variation.
First, take a random sample of 12 schools from the list of unique school ids:</p>
<pre><code class="r">schools = sample(unique(popdata$school), size=12, replace=F)
sample = popdata[popdata$school %in% schools, ]
</code></pre>
<p>Now, we can use the <code>xyplot</code> function from the <code>lattice</code> package:</p>
<pre><code class="r">library(lattice)
xyplot(popular~sex|as.factor(school),type=c("p","g","r"), col.line="black", data=sample)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-6"/> </p>
<p>So, (at least in my sample) there is considerable variation: in some schools gender has almost no effect,
but in other schools the slope is relatively steep and generally positive (meaning girls have higher popularity).
Let's test whether a model with a random slope on gender is a significant improvement:</p>
<pre><code class="r">library(texreg)
</code></pre>
<pre><code>## Version: 1.32
## Date: 2014-05-01
## Author: Philip Leifeld (University of Konstanz)
</code></pre>
<pre><code class="r">m2 = lme(popular ~ sex + texp, random=~sex|school, popdata)
anova(m, m2)
</code></pre>
<pre><code>## Model df AIC BIC logLik Test L.Ratio p-value
## m 1 5 4454 4482 -2222
## m2 2 7 4290 4329 -2138 1 vs 2 168.5 <.0001
</code></pre>
<pre><code class="r">screenreg(list(m, m2))
</code></pre>
<pre><code>##
## ==========================================
## Model 1 Model 2
## ------------------------------------------
## (Intercept) 3.56 *** 3.34 ***
## (0.17) (0.16)
## sexgirl 0.84 *** 0.84 ***
## (0.03) (0.06)
## texp 0.09 *** 0.11 ***
## (0.01) (0.01)
## ------------------------------------------
## AIC 4454.36 4289.89
## BIC 4482.36 4329.09
## Log Likelihood -2222.18 -2137.95
## Num. obs. 2000 2000
## Num. groups 100 100
## ==========================================
## *** p < 0.001, ** p < 0.01, * p < 0.05
</code></pre>
<p>So, <code>m2</code> is indeed a significant improvement. </p>
<h1>The lme4 package</h1>
<p><code>lme4</code> is a package that gives a bit more flexibility in specifying time series.
Specifically, it allows us to specify a binomial family, i.e. logistic regression.
The following dichotomized the popularity and checks whether the effect of gender on popularity is dependent on the school:</p>
<pre><code class="r">library(lme4)
</code></pre>
<pre><code>## Loading required package: Matrix
## Loading required package: Rcpp
##
## Attaching package: 'lme4'
##
## The following object is masked from 'package:nlme':
##
## lmList
</code></pre>
<pre><code class="r">popdata$dich = cut(popdata$popular, 2, labels=c("lo","hi"))
m = glmer(dich ~ sex + (1|school), popdata, family="binomial")
m2 = glmer(dich ~ sex + (1 + sex|school), popdata, family="binomial")
summary(m2)
</code></pre>
<pre><code>## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: dich ~ sex + (1 + sex | school)
## Data: popdata
##
## AIC BIC logLik deviance df.resid
## 1536.2 1564.2 -763.1 1526.2 1995
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.781 -0.326 -0.112 0.266 5.314
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## school (Intercept) 8.5 2.91
## sexgirl 3.4 1.84 0.16
## Number of obs: 2000, groups: school, 100
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.097 0.351 -5.97 2.4e-09 ***
## sexgirl 2.858 0.297 9.63 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## sexgirl -0.215
</code></pre>
<pre><code class="r">anova(m, m2)
</code></pre>
<pre><code>## Data: popdata
## Models:
## m: dich ~ sex + (1 | school)
## m2: dich ~ sex + (1 + sex | school)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m 3 1572 1589 -783 1566
## m2 5 1536 1564 -763 1526 39.8 2 2.3e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
</code></pre>
<p>If we would like to see for which schools the effect of gender were the strongest,
we can use the <code>ranef</code> function to get the intercepts and slopes per group, and order them by slope:</p>
<pre><code class="r">effects = ranef(m2)$school
effects = effects[order(effects$sexgirl), ]
head(effects)
</code></pre>
<pre><code>## (Intercept) sexgirl
## 38 1.9160 -3.514
## 53 0.5028 -3.225
## 10 -1.2437 -2.345
## 80 1.9169 -2.132
## 12 0.1725 -2.116
## 61 -0.6707 -1.897
</code></pre>
<pre><code class="r">tail(effects)
</code></pre>
<pre><code>## (Intercept) sexgirl
## 32 -0.7054 1.753
## 8 0.4938 1.758
## 7 0.2000 1.798
## 16 0.5682 1.872
## 54 -0.4788 2.132
## 52 -0.4730 2.362
</code></pre>
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