Mixed Poisson regression models for tree mortality in even-aged forests

Reliable models of the distribution of tree mortality over time and across stand conditions are necessary for sound management of even-aged forests. This dissertation examines a nonlinear regression framework for modeling periodic stand-level mortality data, which tend to be highly variable, skewed, and frequently contain many zero outcomes. Variability about large-scale trends is structured according to probability distributions based on mixtures of Poisson mass functions that allow for flexible mean-variance relationships, latent ecological processes; and unmeasured heterogeneity across observations and clusters of observations. Attention is focused on whether these models can adequately characterize distributional features of stand-level mortality data and on the models' implications with regards to the use of data in parameter estimation.; Models are developed and fit to mortality data from a loblolly pine ( Pinus taeda L.) spacing trial composed of 192 plots monitored annually over two decades. Mixture models that allow for extra-Poisson variation fit these data well, accounting for heteroscedasticity and a large zero fraction. Certain hurdle and zero-inflated specifications offer an improved fit but do not admit a well-defined ecological interpretation, calling into question the validity of the associated estimation procedures in this context. Two-component finite mixture models, composed of non-degenerate distributions linked by a submodel for the intensity of tree crowding, permit identification of background and self-thinning rates of mortality and offer a more compelling basis for estimation and inference. Allowing subsets of model parameters to vary randomly among clusters of observations provides a parsimonious description of unmeasured heterogeneity in the distribution of periodic mortality and improves model-data agreement considerably.