Bayesian Models for Repeated Measures Data Using Markov Chain Monte Carlo Methods
Abstract
Bayesian models for repeated measures data are fitted for three different data sets. Markov Chain Monte Carlo (MCMC) methodology is applied to each case with Gibbs sampling and/or an adaptive Metropolis-Hastings (MH) algorithm used to simulate the posterior distribution of parameters.
The first project models the variance pattern over 8 years and determines if the pattern changed between the before and after regulatory change periods. Companies were grouped into four groups based on market capitalization and on industry regulation. Block structures and linear models for variances were proposed to estimate covariance structures. Results: block variance-covariance structures with a linear model for variances within each group of years improved the model fit compared with basic structures.
The second project uses data for the “Cyber-enabled learning: Digital Natives in Integrated Scientific Inquiry Classrooms” project. The objective was to determine whether teacher professional development (PD) utilizing cyber-enabled resources lead to meaningful student learning outcomes measured by student end-of-year CRT scores for students with teachers who underwent PD. We used a Bayesian hierarchical model with latent teacher effects predicted by repeated measures on self-reported and observed instruments for PD teachers. Results: the Bayesian hierarchical model successfully predicted the teacher effects with selected instrument predictors using Bayesian variable selection.
The third project looked at the existence and dollar amount of healthcare expenditures for three 2-year periods for a group of subjects with the same health insurance plan. Bayesian two-part models with random effects were used to model how the likelihood of expenditures and the actual expenditures, conditional on positive expenditures, depended on Body Mass Index (BMI), adjusting for age, gender, and smoking status. Results: there was a strong correlation between the probability of health care expenditures and dollar amount spent given expenditures. Smokers had a higher risk of expenditures. The rate of increase on risk of health care expenditures for extreme BMI was greater in later years than in the 2-year baseline for nonsmokers, but high at all times for smokers.