Small Sample Power Characteristics of Generalized Mixed Model Procedures for Binary Repeated Measures Data Using Sas

Abstract

Researchers in the agricultural and biological sciences often conduct experiments with repeated measures and categorical response variables. Recent advances in statistical computing have made several options available to analyze data from these experiments. For example, SAS has several procedures based on generalized mixed model theory. These include PROC GENMOD, MIXED, NLMIXED, and the GLIMMIX macro. Inference for these procedures depends on asymptotic theory. While statistics literature contains some information about the small-sample behavior, there is much that remains unknown. This presentation will focus on Bernoulli response variables. Power characteristics are compared via simulation for several scenarios involving relatively small repeated measures experiments.

Analyzing Binomial Data in a Split-Plot Design: Classical Approaches or Modern Techniques?

“…The results in this study indicate that methods with mixed or generalized linear mixed models, where random effects are modeled directly, hold Type I error rates better than the methods with generalized linear models, which model non-normality but not random effects. This finding is similar to the one found by Grossardt (2003) for analyzing Poisson data in a split-plot design, by Beckman and Stroup (2003) for analyzing binary repeated-measures data, and by Sui and Stroup (2001) for analyzing multinomial repeated-measures data. T-tests done to test the factor effects show that the main effects of µ, K, and s are possibly significant for the three methods that best maintain their error rates (MIXED, MIXEDT, and GLMM).…”

“…Nonetheless, these results, along with those of Grossardt (2003), Beckman and Stroup (2003), and Sui and Stroup (2001) provide evidence to suggest that normal-based mixed model procedures are reasonably robust against deviations from normality. Also, it appears that proper modeling of random effects is much more important in an analysis than exactly matching the parent distribution of the data.…”

“…Grossardt (MS report, 2003) studies Type I error rates of eleven methods for analyzing count data in split-plot designs and finds that mixed model methods and the generalized linear mixed model method maintain Type I error rates better than generalized linear model methods that have no mechanism to account for random effects. Beckman and Stroup (2003) and Sui and Stroup (2001) compare five methods for analyzing binomial or multinomial data in repeated measures experiments where the issues of non-normality and correlated measurements occur. They find similarly that the classical mixed model approach performs better than methods based on the generalized linear and generalized linear mixed models.…”