Statistical methods for count data from designs with nested structure

Count data from nested designs, split-plot experiments, and repeated measures studies are commonly encountered in agricultural and ecological research. Such data are often analyzed using analysis of variance methods based on distributional assumptions that may not be valid for count data, especially when expected counts are small. Furthermore, inferences for generalized linear models, such as log-linear and logistic regression models, are generally based on an assumption of independent Poisson or binomial counts that does not adequately account for correlations and heterogeneity arising in count data from nested designs. Recent developments for generalized linear mixed models, quasi-likelihood estimation and robust covariance estimation have provided new tools for analyzing such data. The objectives of this dissertation are to develop and refine statistical methods for analyzing count data from nested designs, illustrate the use of these methods in agricultural and ecological studies, and determine conditions under which these methods are appropriate;Various approaches for analyzing count data from nested designs are illustrated using studies on corn borer control, bird abundance, and nest predation. One approach uses maximum likelihood estimation based on an incorrect assumption of independent counts in conjunction with robust estimation of the covariance matrix of the parameter estimates. A second approach applies quasi-likelihood estimation to generalized linear mixed models. We consider both method of moments and approximate restricted maximum likelihood (REML) estimation of variance components. We also compare these approaches to analysis of variance using both the original and transformed counts;Based on results from the first two examples, simulation studies were performed to investigate small sample performance of the estimation procedures. For split-plot designs performed in blocks, using too few blocks results in underestimation of the variance component for blocks and a corresponding underestimation of the intercept in generalized linear mixed models. This results in underestimation of standard errors and reduced coverage probabilities of confidence intervals for whole-plot effects, but inferences for sub-plot effects are not as dramatically affected. Simple analysis of variance procedures are shown to perform reasonably well and should not be automatically ruled out for count data