Date of Award
Doctor of Philosophy
The work presented in this dissertation focuses on developments allowing for more effective exploration of the model space of mixed models. Mixed models were developed to appropriately represent the dependence structure expected when data are organized in groups. They incorporate parameters that govern the dependence structure—the random effects—and parameters that govern the global trend—fixed effects. With the additional flexibility provided by the random effects comes additional complexity at each stage of statistical modeling. The problem of parameter estimation, i.e., model fitting, has been widely addressed in the literature, with the most commonly used approaches being maximum likelihood estimation and restricted maximum likelihood estimation. The problem of model checking is less developed. In this dissertation we present a unified framework for residual and influence analysis overcoming the fragmented nature of the literature and an R package that provides open source diagnostic tools for this class of model. Additionally, we discuss the effect of confounding on the distributions of the random effects and present an approach based on the generalized eigenvalue decomposition to decouple random effects from different levels. Finally, we illustrate the use of visual inference for model selection and diagnosis in situations where conventional tests break down. To keep the covariance structure at a manageable complexity, we restrict attention to linear mixed models with nested data structures, which are commonly referred to as either hierarchical linear models or multilevel linear models.
Adam Madison Montgomery Loy
Loy, Adam Madison Montgomery, "Diagnostics for mixed/hierarchical linear models" (2013). Graduate Theses and Dissertations. 13277.