Subject-Specific prediction using a nonlinear mixed model: Consequences of different approaches

Abstract

Nonlinear mixed models can be used for subject-specific prediction of response values, after an observation on a new subject has been made, using conditional expectation. In forest modeling, a typical example of this is the application of a previously fitted model to a new set of stand or tree data that is in the population of modeling data but was not used in the initial estimation of the model parameters. In the linear case, this is simplified to finding first a prediction for the random effects involved, a technique known as calibration or localization, but in the nonlinear case it is not possible to use any single prediction of the random effects. Instead, the prediction involves a ratio of integrals, which can be approximated by linearizing the nonlinear mean function, as is conventionally done in forest modeling, or computed numerically using integral approximation. Details of the problem and the solutions are covered, and confidence of the predictions is briefly discussed in this article. Consequences of the different solutions are also investigated by examples on the prediction of stand dominant height.