The analysis of longitudinal ordinal data

Longitudinal data, in which a series of observations is collected on a typically large number of experimental units is one of the most frequent and important sources of quantitative information in forestry. The dependencies among repeated observations for an experimental unit must be accounted for in order to validate statistical estimation and inference in modeling efforts. The recent advances in statistical theory for correlated data created a body of theory which will become of increasing importance as analysts realize the limitations of traditional methods that ignore these dependencies. Longitudinal data fosters research questions that focus on the individual experimental unit rather than the population as in classical cross-sectional data analysis. Mixed model techniques have emerged as powerful tools to address research problems of this kind and are treated extensively in this dissertation.

Over the last years interest in modeling quantal responses that take on only a countable, discrete number of possible values has also increased throughout the discipline. The theory of generalized linear models provides the groundwork to embody quantal response models into the toolbox of applied analysts.

The focus of this dissertation is to combine modern analytical tools for longitudinal data with regression methods for quantal responses. Special emphasis is placed on ordinal and binary data because of their prevalence in ecological, biological, and environmental statistics. The first chapters review the literature and introduce necessary theory. The second part of this dissertation consists of a case study in which binary and ordinal fusiform rust response on loblolly and slash pine is modeled in a longitudinal data base provided by the East Texas Pine Plantation Research Project.