Parameter estimation of two-level nonlinear mixed effects models using first order conditional linearization and the EM algorithm
Multi-level nonlinear mixed effects (ML-NLME) models have received a great deal of attention in recent years because of the flexibility they offer in handling the repeated-measures data arising from various disciplines. In this study, we propose both maximum likelihood and restricted maximum likelihood estimations of ML-NLME models with two-level random effects, using first order conditional expansion (FOCE) and the expectationmaximization (EM) algorithm. The FOCEEM algorithm was compared with the most popular Lindstrom and Bates (LB) method in terms of computational and statistical properties. Basal area growth series data measured from Chinese fir (Cunninghamia lanceolata) experimental stands and simulated data were used for evaluation. The FOCEEM and LB algorithms given the same parameter estimates and fit statistics for models that converged by both. However, FOCEEM converged for all the models, while LB did not, especially for the models in which two-level random effects are simultaneously considered in several base parameters to account for between-group variation. We recommend the use of FOCEEM in ML-NLME models, particularly when convergence is a concern in model selection.
two-level nonlinear mixed effects models first order conditional expansion cunninghamia lanceolata simulated data expectationmaximization algorithm lindstrom and bates algorithm