Jeffrey S. Simonoff
New York University

Regression tree-based diagnostics for linear multilevel models

Multilevel models have gained prominence in the past 30 years as a systematic way of analyzing hierarchical or clustered data. Common examples include longitudinal data (where multiple measurements over time are made on individuals), educational data (where students are nested within classes, which are nested within schools, and so on), and biomedical data (where offspring are clustered within families). In order to account for this structure such models include both fixed effects designed to represent population-level relationships and random effects designed to represent within-individual (cluster) effects. Linear multilevel models are a standard special case, where fixed effects are defined using a linear function of known covariates, but as is true of any model, if underlying assumptions do not hold its use can lead to misleading inferences. In this talk I describe how a recently-proposed adaptation of regression trees to hierarchical data (termed RE-EM trees) can be used to construct diagnostics for various linear multilevel model assumptions, including linearity and homoscedasticity. The properties of such diagnostics are examined through both Monte Carlo simulations and application to real data examples.