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.