Poisson mixture models for regression analysis of stand-level mortality

Periodic stand-level mortality data from permanent plots lend to be highly variable, skewed, and frequently contain many zero observations. Such data have commonly been modeled using nonlinear mortality functions fitted by least squares, and more recently by a two stage approach incorporating a logistic regression step. This study describes a set of nonlinear regression models that structure stochastic variation about a mortality function according to basic probability distributions appropriate for non-negative count data, including the Poisson, negative binomial (NB), and generalized Poisson (GP). Also considered are zero-inflated and hurdle modifications of these basic models. The models are developed and fit to mortality data from a loblolly pine (Pinus taeda L.) spacing trial with a conspicuous mode at 0. The sample data exhibit more variability than can be accommodated by a Poisson or modified Poisson model; the NB and GP models incorporate the extra-Poisson dispersion and offer an improved fit. A hurdle NB model best describes this sample, but, like the zero-inflated models and two-stage approach, modifies the interpretation of the mean structure and raises the question of overriding. Considering both data-model agreement and the biological relevance of these models' components, the analysis suggests that the NB model offers a more compelling and credible inferential basis for fitting stand-level mortality functions.