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R Textbook Examples
Multilevel Analysis Techniques and Applications by Joop Hox
Chapter 4: Some Important Methodological and Statistical Issues

library(foreign)
library(lme4)

Table 4.1 on page 57 using the popular dataset.

popdata<-read.dta("http://www.ats.ucla.edu/stat/stata/examples/mlm_ma_hox/popular.dta")
Part 1
m4.1.1 <- lmer(popular~sex + (1|school), popdata)
summary(m4.1.1)

Linear mixed model fit by REML 
Formula: popular ~ sex + (1 | school) 
   Data: popdata 
  AIC  BIC logLik deviance REMLdev
 4501 4523  -2246     4485    4493
Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.86222  0.92856 
 Residual             0.45992  0.67817 
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  4.89722    0.09529   51.39
sexgirl      0.84370    0.03096   27.25

Correlation of Fixed Effects:
        (Intr)
sexgirl -0.158
Part 2
attach(popdata)
sex01 <- 1*(sex=="girl")

csex <- sex01 - mean(sex01)
m4.1.2 <- lmer(popular~csex + (1|school))
summary(m4.1.2)

Linear mixed model fit by REML 
Formula: popular ~ csex + (1 | school) 
  AIC  BIC logLik deviance REMLdev
 4501 4523  -2246     4485    4493
Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.86222  0.92856 
 Residual             0.45992  0.67817 
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.30810    0.09409   56.41
csex         0.84370    0.03096   27.25

Correlation of Fixed Effects:
     (Intr)
csex 0.000
Part 3
m4.1.3 <- lmer(popular~sex + (sex|school))
summary(m4.1.3)

Linear mixed model fit by REML 
Formula: popular ~ sex + (sex | school) 
  AIC  BIC logLik deviance REMLdev
 4348 4382  -2168     4330    4336
Random effects:
 Groups   Name        Variance Std.Dev. Corr   
 school   (Intercept) 0.94027  0.96968         
          sexgirl     0.27252  0.52203  -0.279 
 Residual             0.39244  0.62645         
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  4.89009    0.09902   49.39
sexgirl      0.84311    0.05964   14.14

Correlation of Fixed Effects:
        (Intr)
sexgirl -0.307
Part 4
m4.1.4 <- lmer(popular~csex + (csex|school))
summary(m4.1.4)

Linear mixed model fit by REML 
Formula: popular ~ csex + (csex | school) 
  AIC  BIC logLik deviance REMLdev
 4348 4382  -2168     4330    4336
Random effects:
 Groups   Name        Variance Std.Dev. Corr   
 school   (Intercept) 0.86758  0.93144         
          csex        0.27252  0.52204  -0.017 
 Residual             0.39244  0.62645         
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.30068    0.09424   56.24
csex         0.84311    0.05963   14.14

Correlation of Fixed Effects:
     (Intr)
csex -0.015
Table 4.2 on page 60, continuing to use the popular dataset.
Part 1
m4.2.1 <- lmer(popular~sex + texp + (1 + sex|school))
summary(m4.2.1)

Linear mixed model fit by REML 
Formula: popular ~ sex + texp + (1 + sex | school) 
  AIC  BIC logLik deviance REMLdev
 4290 4329  -2138     4261    4276
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.41158  0.64155        
          sexgirl     0.27329  0.52278  0.062 
 Residual             0.39248  0.62648        
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  3.34001    0.16079   20.77
sexgirl      0.84315    0.05969   14.13
texp         0.10835    0.01022   10.61

Correlation of Fixed Effects:
        (Intr) sexgrl
sexgirl -0.020       
texp    -0.908  0.000
Part 2
m4.2.2 <- lmer(popular~sex + texp + sex*texp + (1 + sex|school))
summary(m4.2.2)

Linear mixed model fit by REML 
Formula: popular ~ sex + texp + sex * texp + (1 + sex | school) 
  AIC  BIC logLik deviance REMLdev
 4284 4329  -2134     4246    4268
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.41198  0.64186        
          sexgirl     0.22641  0.47582  0.077 
 Residual             0.39241  0.62643        
Number of obs: 2000, groups: school, 100

Fixed effects:
              Estimate Std. Error t value
(Intercept)   3.313521   0.161017  20.579
sexgirl       1.329594   0.133052   9.993
texp          0.110235   0.010232  10.773
sexgirl:texp -0.034035   0.008457  -4.024

Correlation of Fixed Effects:
            (Intr) sexgrl texp  
sexgirl     -0.046              
texp        -0.909  0.042       
sexgirl:txp  0.042 -0.908 -0.046
Part 3
ctexp <- texp - mean(texp)
m4.2.3 <- lmer(popular~csex + ctexp + (1 + csex|school))
summary(m4.2.3)

Linear mixed model fit by REML 
Formula: popular ~ csex + ctexp + (1 + csex | school) 
  AIC  BIC logLik deviance REMLdev
 4290 4329  -2138     4261    4276
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.49674  0.70480        
          csex        0.27330  0.52278  0.418 
 Residual             0.39248  0.62648        
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.29601    0.07193   73.63
csex         0.84315    0.05969   14.13
ctexp        0.10835    0.01022   10.61

Correlation of Fixed Effects:
      (Intr) csex  
csex   0.359       
ctexp -0.005  0.000
Part 4
m4.2.4 <- lmer(popular~csex + ctexp + csex*ctexp + (1 + csex|school))
summary(m4.2.4)

Linear mixed model fit by REML 
Formula: popular ~ csex + ctexp + csex * ctexp + (1 + csex | school) 
  AIC  BIC logLik deviance REMLdev
 4284 4329  -2134     4246    4268
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.48849  0.69892        
          csex        0.22641  0.47583  0.402 
 Residual             0.39241  0.62643        
Number of obs: 2000, groups: school, 100

Fixed effects:
             Estimate Std. Error t value
(Intercept)  5.296908   0.071346   74.24
csex         0.844154   0.055616   15.18
ctexp        0.093660   0.010851    8.63
csex:ctexp  -0.034035   0.008457   -4.02

Correlation of Fixed Effects:
           (Intr) csex   ctexp 
csex        0.338              
ctexp      -0.005 -0.002       
csex:ctexp -0.002 -0.004  0.336
Figure 4.3 on page 61.
m4.3 <- lmer(popular~sex + texp + sex*texp + (1 + sex|school))
sextexp = texp * sex01
linp <- fixef(m4.3)[1] + fixef(m4.3)[2]*sex01 + fixef(m4.3)[3]*texp + fixef(m4.3)[4]*sex01*texp
 
plot(x = texp[sex01==1], y = linp[sex01==1], type = "l", 
xlab = "teacher experience in years", ylab = "predicted values",
xlim = c(0,30), ylim = c(3.5, 7), col = "red")
points(x = texp[sex01==0], y = linp[sex01==0], type = "l", col = "blue")
legend("bottomright", c("girls", "boys"), col = c("red", "blue"), lty = c(1,1))
Table 4.3 on page 63, continuing to use the popular dataset.
Part 1
m4.3.1 <- lmer(popular~ (1 |school))
summary(m4.3.1)

Linear mixed model fit by REML 
Formula: popular ~ (1 | school) 
  AIC  BIC logLik deviance REMLdev
 5122 5138  -2558     5113    5116
Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.87981  0.93798 
 Residual             0.63868  0.79917 
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)   5.3076     0.0955   55.58
Part 2
m4.3.2 <- lmer(popular~ sex + (1 |school))
summary(m4.3.2)

Linear mixed model fit by REML 
Formula: popular ~ sex + (1 | school) 
  AIC  BIC logLik deviance REMLdev
 4501 4523  -2246     4485    4493
Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.86222  0.92856 
 Residual             0.45992  0.67817 
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  4.89722    0.09529   51.39
sexgirl      0.84370    0.03096   27.25

Correlation of Fixed Effects:
        (Intr)
sexgirl -0.158
Part 3
m4.3.3 <- lmer(popular~ sex + texp + (1 |school))
summary(m4.3.3)

Linear mixed model fit by REML 
Formula: popular ~ sex + texp + (1 | school) 
  AIC  BIC logLik deviance REMLdev
 4454 4482  -2222     4429    4444
Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.48596  0.69711 
 Residual             0.45992  0.67818 
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  3.56068    0.17147   20.77
sexgirl      0.84467    0.03095   27.29
texp         0.09345    0.01085    8.61

Correlation of Fixed Effects:
        (Intr) sexgrl
sexgirl -0.088       
texp    -0.905  0.000
Part 4
m4.3.4 <- lmer(popular~ sex + texp + (1 + sex|school))
summary(m4.3.4)

Linear mixed model fit by REML 
Formula: popular ~ sex + texp + (1 + sex | school) 
  AIC  BIC logLik deviance REMLdev
 4290 4329  -2138     4261    4276
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.41158  0.64155        
          sexgirl     0.27329  0.52278  0.062 
 Residual             0.39248  0.62648        
Number of obs: 2000, groups: school, 100

Fixed effects:
            Estimate Std. Error t value
(Intercept)  3.34001    0.16079   20.77
sexgirl      0.84315    0.05969   14.13
texp         0.10835    0.01022   10.61

Correlation of Fixed Effects:
        (Intr) sexgrl
sexgirl -0.020       
texp    -0.908  0.000
Part 5
m4.3.5 <- lmer(popular~ sex + texp + sex*texp + (1 + sex|school))
summary(m4.3.5)

Linear mixed model fit by REML 
Formula: popular ~ sex + texp + sex * texp + (1 + sex | school) 
  AIC  BIC logLik deviance REMLdev
 4284 4329  -2134     4246    4268
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 school   (Intercept) 0.41198  0.64186        
          sexgirl     0.22641  0.47582  0.077 
 Residual             0.39241  0.62643        
Number of obs: 2000, groups: school, 100

Fixed effects:
              Estimate Std. Error t value
(Intercept)   3.313521   0.161017  20.579
sexgirl       1.329594   0.133052   9.993
texp          0.110235   0.010232  10.773
sexgirl:texp -0.034035   0.008457  -4.024

Correlation of Fixed Effects:
            (Intr) sexgrl texp  
sexgirl     -0.046              
texp        -0.909  0.042       
sexgirl:txp  0.042 -0.908 -0.046
Table 4.4 on page 70--we have skipped this table for now.

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