Accounting for Structure in Mixed/Hierarchical Models

Abstract

AbstractThis chapter defines the fixed (population-level) and random (group-level) effects of categorical explanatory variables in the frequentist and Bayesian frameworks. These effects allow models to account for structure in the data induced by the experimental or survey design, or by the sampling methods. The chapter carefully discusses the interpretation of estimated random (group-level) intercepts and slopes in linear mixed models, and the ambiguities, problems, and controversies related to the definition and interpretation of random effects in the frequentist framework. It illustrates the “shrinkage effect” and its importance in mixed/hierarchical models, and covers the controversies about model selection and the statistical significance of fixed effects in frequentist mixed models, including the use of the Satterwhaite and Kenward–Roger corrections, and the parametric bootstrap. All statistical models are fitted in both the frequentist and Bayesian frameworks.