Maximum likelihood estimation for predicting the probability of obtaining variable shortleaf pine regeneration densities

Abstract

A logistic equation is the basis for a model that predicts the probability of obtaining regeneration at specified densities. The density of regeneration (trees/ha) for which an estimate of probability is desired can be specified by means of independent variables in the model. When estimating parameters, the dependent variable is set to 1 if the regeneration density (trees/ha) on the plot is greater than the specified density (trees/ha), otherwise 0. Since it is desired to estimate parameters for a range of probability densities, traditional estimation techniques for logistic models cannot be used. Multiple regeneration densities require a multinomial distribution, for which maximum likelihood estimates are obtained. Counts of shortleaf pine regeneration taken 9-10 years after thinning on 182 plots established in naturally occurring shortleaf pine forests are used to estimate parameters.