Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments

Abstract

A modified Richard's growth model with nonlinear mixed effects is developed for modeling slash pine (Pinus elliottii Engelm.) dominant height growth in conjunction with different silvicultural treatments. All three parameters in the model turn out to have both fixed and random individual plot or silvicultural treatments effects. Moving average correlation with 2° was identified as within-plot error structure. The advantages of the mixed effects model in prediction for new responses are demonstrated in detail by formulations and examples. The modified Richards model has a form that combines dominant height growth and site index into one model form, so the incompatibility between height growth and site index model can be avoided. The general methodologies of nonlinear mixed effects model building, such as which parameters in the model should be considered to be random and which should be purely fixed, how to determine appropriate within-plot variance covariance structure, and how to specify between-plot variation via appropriate covariate modeling, are addressed in detail. Likelihood ratio test and Akaike information criterion (AIC) are used in model performance evaluation. Some useful graphical model diagnosis tools are also presented.