Estimation in Forest Yield Models Using Composite Link Functions with Random Effects

Abstract

A sigmoidal forest yield model is estimated from longitudinal measurements of sample plots where measurement times and intervals vary. The projection form of the yield model is fitted as a generalized linear model (GLM) with composite link functions and an offset. This allows age and additional covariates to be easily incorporated in a more flexible nonlinear structure than that provided by single link GLMs. Also, existing algorithms for fitting generalized linear mixed models (GLMMs) are easily adapted to fit the projection model, thereby allowing incorporation of random plot effects. Estimation for the composite link GLMM is described, as well as an alternative to the GLMM in which random effects are incorporated as linear components on the same scale as the response. This model is referred to as an additive generalized linear mixed model (AGLMM). Unlike the GLMM, the fixed-effect parameter estimates in the AGLMM are population-average (PA). The AGLMM is fitted using a modification of a subject-specific (SS) algorithm using marginal expectation. The random effects in the AGLMM may have a natural interpretation or may provide a means of generating a marginal covariance structure, as is the case with linear mixed models. A simple example of an AGLMM for binomial data and logit link is given. In both this and the forest yield example, a single, artificial random effect is constructed to give exchangeable correlation for observations within-subjects and a comparison of fit of the AGLMM and GLMM is made using a conditional quasi-deviance. If the fit is similar and PA parameter estimates are required, the AGLMM is preferred.