On the statistical and biological behaviors of nonlinear mixed forest models

Abstract

This study examined both statistical and biological behaviors of two nonlinear mixed models fitted by the first-order (FO) and first-order conditional expectation (FOCE) methods. The simpler FO method was found to alter the mathematical forms of the base models and produce biologically unreasonable predictions for some subjects. This was not the case for the more complex FOCE method. Since the computations for predicting random parameters and for making subject-specific (SS) predictions were different for the two methods, mixing them would potentially produce large prediction biases and unexpected biological behaviors. This was demonstrated on two data sets (basal area–age and height–diameter data sets). For basal area–age data, accurate and precise basal area predictions were produced as long as a consistent method was used for predicting random parameters and for making SS predictions, regardless of the method used for model fitting. Otherwise, less accurate and precise predictions were produced, with some predictions totally against biological expectations. For height–diameter data, both consistent and inconsistent methods produced similar prediction statistics, but this does not mean that inconsistent methods should be adopted. Overall the FOCE method was found to be superior to the FO method in terms of producing biologically more reasonable predictions.