Abstract: [Objective] Fitting non-linear mixed effects models (NLME), predicting the random effects parameters, as well as predicting the response variable, often involve a Taylor series expansion for linearization, based upon either the expected value of the random effects or final iterative value. In forestry, however, the linearization bases are not always consistent as they should be, and probably reduced the accuracy of prediction. In this paper, we investigated the tree height growth and discussed the effects of inconsistency among the linearization bases for fitting, predicting random effects the response.[Method] We randomly selected 49 trees for NLME-fitting and 30 trees for validation from 79 dominant trees of ponderosa pine in British Columbia, Canada. The base model was three-parameter Logistic. We used the nlme function in R and the nlmixed procedure in SAS for model fitting, respectively corresponding linearization based upon the expected value and the final iterative value. The IML procedure in SAS was employed for predicting the random effects and the response. Mean squared prediction error (MSPE), mean percentage error (MPE), and mean absolute percentage error (MAPE) were used as evaluation criteria.[Result] The results showed that inconsistent linearization bases between the random effects and the response significantly decreased the accuracy of the response prediction.[Conclusion] The linearization bases between the random effects and the response had to be consistent, and enough for obtaining predictions as accurate as possible. The accuracy of prediction was invariant to the linearization base for model-fitting and to either the expected value or the final iterative value, which was used as a linearization base.

Key words: non-linear mixed effects(NLME), growth and yield prediction, Logistic function