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 discipline...
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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 expectation-maximization (EM) algorithm. The FOCE EM 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 FOCE EM and LB algorithms given the same parameter estimates and fit statistics for models that converged by both. However, FOCE EM 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 FOCE EM in ML-NLME models, particularly when convergence is a concern in model selection. (C) 2013 Elsevier B.V. All rights reserved.
Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of...
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Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of NLME models using first-order conditional expansion (FOCE) and the expectationmaximization (EM) algorithm. The FOCE-EM algorithm implemented in the ForStat procedure SNLME is compared with the lindstrom and bates (LB) algorithm implemented in both the SAS macro NLINMIX and the S-Plus/R function nlme in terms of computational efficiency and statistical properties. Two realworld data sets an orange tree data set and a Chinese fir (Cunninghamia lanceolata) data set, and a simulated data set were used for evaluation. FOCE-EM converged for all mixed models derived from the base model in the two realworld cases, while LB did not, especially for the models in which random effects are simultaneously considered in several parameters to account for between-subject variation. However, both algorithms had identical estimated parameters and fit statistics for the converged models. We therefore recommend using FOCE-EM in NLME models, particularly when convergence is a concern in model selection.
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