Table 7.1 on page 126 using the pupcross dataset.
Part 1: Intercept only.
library(foreign) library(lme4) pupcross<-read.dta("https://stats.idre.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