Stepwise model building for mixed-effects models with random scale effects

Lei Shu, Purdue University

Abstract

The use of mixed-effects models in practice, often in the form of Bayesian hierarchical models, is growing rapidly because of major developments in computational methods for these models. Mixed-effects models with measurements of a response on a continuous measurement scale typically specify the random effects as location effects. Data sets with random location effects can also have random scale effects. When scale effects are present, it is essential to model them to insure valid inferences. But typically, in practice, the random location effects and errors are taken to be normal and the random scale effects are taken to be the square root of an inverse gamma. However, these assumptions are usually driven by convenience and not reality. Little previous work has been done in model building for mixed-effects models with random scale effects because adding a random scale effect into the usual mixed-effects model will lead to a great challenge. But assessing the plausibility of a posited model is always fundamental, especially in Bayesian data analysis. A Bayesian analysis, which conditions on the whole probability model, can be very misleading when the model is far from plausible. This dissertation introduces a stepwise model building approach for the mixed-effects models with random scale effects. The stepwise model building approach is able to check and identify the distribution for each model component step by step. New data visualization tools, immensely powerful for model building, have been developed. In field null-power simulations are performed to ensure the effectiveness of the visualization tools.

Degree

Ph.D.

Advisors

Cleveland, Purdue University.

Subject Area

Statistics

COinS