Qualitative response models theory and its application to forestry

The focus of this dissertation is the theory of qualitative response models and its application to forestry related problems. Qualitative response models constitute a class of regression models used for predicting the result in one of a discrete number of mutually exclusive outcomes. These models, also known as discrete regression models, differ from the usual continuous regression models in that the response variable takes only discrete values. In forestry applications the use of such models has been largely confirmed to mortality studies where only the simplest kind of qualitative response models - a dichotomous (binary) dependent variable model - is applied. However, it is common in forestry to deal with many variables which are either discrete or recorded discretely and need to be formulated by more complex models involving polychotomous dependent variables. The estimation of such complex qualitative response models only recently has been made possible by the development of advanced computer technology.

The first objective of this study was to specify dichotomous and polychotomous response models that appear to be suitable for forestry applications and present methods of statistical analysis for these models. The models considered in this study were: the linear probability model, binary logit and probit, ordered and unordered multinomiallogit and probit and McFadden's conditionallogit. Special attention was paid to the following problems: i) how to motivate a qualitative response model which is theoretically correct and statistically manageable, ii) how to estimate and draw inferences about the model parameters, iii) what criteria to use when choosing among competing models and iv) how to detect outlying, high leverage and highly influential observations.

The second objective was to exemplify the utility of the above models by considering two, forestry related, case studies. Assessing the merchantability of loblolly pine trees growing on plantations in southern United States and modelling the incidence and spread of fusifonn rust on loblolly and slash pine plantations in east Texas. The results demonstrated the potential of qualitative response models for meaningful implementation in a variety of forestry applications and also, suggested topics for future research work.