Multilevel Modeling Using R and lmer

Douglas Bates

Multilevel models, which take into account different sources (or levels) of variation affecting the response, are used in many different applications areas including education (value-added modeling of annual test scores such as are mandated by the No Child Left Behind Act), sociology and psychology, agricultural experiments (data from split-plot and strip-plot designs), animal breeding (breeding values of animals taking pedigree into account) and bioinformatics (models of gene effects in microarray data).

To statisticians these are all examples of mixed-effects models or, more simply, mixed models (as in SAS PROC MIXED, one of the workhorses of statistical analysis for those who choose to use SAS). Two of the greatest challenges in fitting linear mixed models and generalized linear mixed models - working with very large data sets and fitting models with crossed or partially crossed groupings of random effects - are addressed by the lmer function in the lme4 package.

In this workshop we introduce such models and illustrate the use of lmer for fitting and evaluating linear mixed models (LMMs) and generalized linear mixed models (GLMMs). These models will be applied to large data sets with complex structure and the usual warts encountered with real-world data. You will also learn lattice graphics techniques for examining data with multiple levels of variation and the use of Markov chain Monte Carlo techniques for assessing the variability of the parameter estimates from multilevel models.