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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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