Robustness of Generalized Linear Mixed Models for Split-Plot Designs with Binary Data

Abstract

This paper examined the robustness of the generalized linear mixed model (GLMM). The GLMM estimates fixed and random effects, and it is especially useful when the dependent variable is binary. It is also useful when the dependent variable involves repeated measures, since it can model correlation. The present study used Monte Carlo simulation to analyze the empirical Type I error rates of GLMMs in split-plot designs. The variables manipulated were sample size, group size, number of repeat-ed measures, and correlation between repeated measures. Extreme condi-tions were also considered, including small samples, unbalanced groups, and different correlation in each group (pairing between group size and correlation between repeated measures). For balanced groups, the results showed that the group effect was robust under all conditions, while for unbalanced groups the effect tended to be conservative with positive pair-ing and liberal with negative pairing. Regarding time and interaction ef-fects, the results showed, for both balanced and unbalanced groups, that: (a) The test was robust with low correlation (.2), but conservative for me-dium values of correlation (.4 and .6), and (b) the test tended to be con-servative for positive and negative pairing, especially the latter.