Hierarchical Linear Modeling

basic model fitting

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The primary packages for fitting hierarchical (alternatively "mixed" or "multilevel") linear models in R are nlme (older) and lme4 (newer). These packages differ in many minor ways but should generally result in very similar fitted models.

m1.nlme <- lme(Reaction~Days,random=~Days|Subject,data=sleepstudy,method="REML")
m1.lme4 <- lmer(Reaction~Days+(Days|Subject),data=sleepstudy,REML=TRUE)
## [1] TRUE

Differences to consider:

  • formula syntax is slightly different
  • nlme is (still) somewhat better documented (e.g. Pinheiro and Bates 2000 Mixed-effects models in S-PLUS; however, see Bates et al. 2015 Journal of Statistical Software/vignette("lmer",package="lme4") for lme4)
  • lme4 is faster and allows easier fitting of crossed random effects
  • nlme provides p-values for linear mixed models out of the box, lme4 requires add-on packages such as lmerTest or afex
  • nlme allows modeling of heteroscedasticity or residual correlations (in space/time/phylogeny)

The unofficial GLMM FAQ provides more information, although it is focused on generalized linear mixed models (GLMMs).

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