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library(nlme)# data(bdf)## Fit the null model## Compare with Table 4.1, p. 47fm1 <- lme(langPOST ~ 1, data = bdf, random = ~ 1 | schoolNR)VarCorr(fm1)-2*c(logLik(fm1)) # deviance## Fit model with fixed IQ term and random intercept## Compare with Table 4.2, p. 49## From the results in Tables 4.2 and 4.4, it appears that## maximum likelihood fits are used, not REML fits.fm2 <- update(fm1, langPOST ~ IQ.ver.cen)summary(fm2)VarCorr(fm2)-2 * c(logLik(fm2)) # deviance## Purely fixed-effects model for comparison## Compare with Table 4.3, p. 51fm3 <- lm(langPOST ~ IQ.ver.cen, data = bdf)summary(fm3)-2 * c(logLik(fm3)) # deviance## Model with average IQ for the school## Compare with Table 4.4, p. 55fm4 <- update(fm2, langPOST ~ IQ.ver.cen + avg.IQ.ver.cen)summary(fm4)VarCorr(fm4)-2 * c(logLik(fm4)) # deviance