Evaluation of Generalized Linear Mixed Models for Analyzing Disease Incidence Data Obtained in Designed Experiments.

Abstract

Diseased individuals (e.g., leaves, plants) typically are clustered in nature, resulting in greater heterogeneity or variability of disease incidence than would be expected for a random pattern. To account for this variability, as well as the binary nature of disease incidence and the multiple sources of variation in designed experiments, a generalized linear mixed model (GLMM) can be used to analyze collected data. GLMMs are becoming more common in many disciplines and may be preferred over analysis of variance for non-normally distributed data. We evaluated several GLMMs for analyzing the incidence of Phomopsis leaf blight of strawberry in relation to fungicide treatments in five experiments which varied greatly in mean incidence and the differences in incidence between treatments. The first model form accounted for heterogeneity through the residual variance (i.e., the overdispersion parameter), which was assumed to be either fixed for the experiment, or dependent on either treatment or incidence. The second model form accounted for heterogeneity explicitly through a within-plot sampling variance, which was assumed to be either constant or dependent on treatment. All GLMMs could be successfully fitted to the data in each experiment, but there was weak evidence based on the conditional deviance and residual plots that the residual-variance models were more appropriate than the sampling-variance models. Model choice had only a minor effect on F tests for treatment effects and significant differences between treatment means. Based on ease of use and evaluation results, we recommend that the simplest (fixed residual variance) model be used as the first choice in analyzing disease incidence data using GLMMs.