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R Textbook Examples
Multilevel Analysis Techniques and Applications by Joop Hox
Chapter 7: Cross-Classified Multilevel Models

Table 7.1 on page 126 using the pupcross dataset.

Part 1: Intercept only.

library(foreign)
library(lme4)

pupcross<-read.dta("http://www.ats.ucla.edu/stat/stata/examples/mlm_ma_hox/pupcross.dta")

m1<-lmer(achiev ~ (1|sschool) + (1|pschool), pupcross, REML=FALSE)
summary(m1)

Linear mixed model fit by maximum likelihood 
Formula: achiev ~ (1 | sschool) + (1 | pschool) 
   Data: pupcross 
  AIC  BIC logLik deviance REMLdev
 2326 2345  -1159     2318    2321
Random effects:
 Groups   Name        Variance Std.Dev.
 pschool  (Intercept) 0.169348 0.41152 
 sschool  (Intercept) 0.065401 0.25574 
 Residual             0.513169 0.71636 
Number of obs: 1000, groups: pschool, 50; sschool, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept)  6.34865    0.07831   81.07

Part 2: intercept plus pupil level variables

m2<-lmer(achiev ~ pupsex + pupses +(1|sschool) + (1|pschool), pupcross, REML=FALSE)
summary(m2)

Linear mixed model fit by maximum likelihood 
Formula: achiev ~ pupsex + pupses + (1 | sschool) + (1 | pschool) 
   Data: pupcross 
  AIC  BIC logLik deviance REMLdev
 2255 2285  -1122     2243    2258
Random effects:
 Groups   Name        Variance Std.Dev.
 pschool  (Intercept) 0.169009 0.41111 
 sschool  (Intercept) 0.063606 0.25220 
 Residual             0.474255 0.68866 
Number of obs: 1000, groups: pschool, 50; sschool, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.75548    0.10527   54.67
pupsexgirl   0.26131    0.04564    5.73
pupses       0.11409    0.01610    7.09

Correlation of Fixed Effects:
           (Intr) ppsxgr
pupsexgirl -0.254       
pupses     -0.643  0.075

Part 3:  primary by secondary School crossed with pupil and school variables

m3<-lmer(achiev ~ pupsex  + pupses + pdenom + sdenom +(1|sschool) + (1|pschool), pupcross, REML=FALSE)
summary(m3)

Linear mixed model fit by maximum likelihood 
Formula: achiev ~ pupsex + pupses + pdenom + sdenom + (1 | sschool) +      (1 | pschool) 
   Data: pupcross 
  AIC  BIC logLik deviance REMLdev
 2253 2293  -1119     2237    2257
Random effects:
 Groups   Name        Variance Std.Dev.
 pschool  (Intercept) 0.159410 0.39926 
 sschool  (Intercept) 0.055424 0.23542 
 Residual             0.474105 0.68855 
Number of obs: 1000, groups: pschool, 50; sschool, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.51850    0.14077   39.20
pupsexgirl   0.26308    0.04561    5.77
pupses       0.11356    0.01609    7.06
pdenomyes    0.20412    0.12410    1.64
sdenomyes    0.17615    0.09465    1.86

Correlation of Fixed Effects:
           (Intr) ppsxgr pupses pdnmys
pupsexgirl -0.203                     
pupses     -0.472  0.075              
pdenomyes  -0.524  0.021  0.004       
sdenomyes  -0.428  0.003 -0.025 -0.014

Part 4:  primary by secondary School crossed with pupil and school variables with variable pupses being modeled as a random effect.

m4<-lmer(achiev ~ pupsex  + pupses + pdenom + sdenom +(1|sschool) 
                  + (1|pschool) + (pupses|pschool), pupcross, REML=FALSE)
summary(m4)

Linear mixed model fit by maximum likelihood 
Formula: achiev ~ pupsex + pupses + pdenom + sdenom + (1 | sschool) +      (1 | pschool) + (pupses | pschool) 
   Data: pupcross 
  AIC  BIC logLik deviance REMLdev
 2246 2300  -1112     2224    2244
Random effects:
 Groups   Name        Variance  Std.Dev. Corr   
 pschool  (Intercept) 0.0950452 0.308294        
          pupses      0.0080183 0.089545 -0.565 
 pschool  (Intercept) 0.0535395 0.231386        
 sschool  (Intercept) 0.0537343 0.231807        
 Residual             0.4583575 0.677021        
Number of obs: 1000, groups: pschool, 50; sschool, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept)  5.53241    0.13746   40.25
pupsexgirl   0.25316    0.04530    5.59
pupses       0.11423    0.02047    5.58
pdenomyes    0.19990    0.11764    1.70
sdenomyes    0.16456    0.09343    1.76

Correlation of Fixed Effects:
           (Intr) ppsxgr pupses pdnmys
pupsexgirl -0.209                     
pupses     -0.491  0.056              
pdenomyes  -0.512  0.029  0.006       
sdenomyes  -0.432  0.006 -0.020 -0.017

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