Nonlinear mixed models have become popular in forestry applications, and various methods have been proposed for fitting such models. However, it is difficult or even confusing to choose which method to use, and there is not much relevant information available, especially in the forestry context. The main objective of this study was to compare three commonly used methods for fitting nonlinear mixed models: the first-order, the first-order conditional expectation, and the adaptive Gaussian quadrature methods. Both the maximum likelihood and restricted maximum likelihood parameter estimation techniques were evaluated. Three types of data common in forestry were used for model fitting and model application. It was found that the first-order conditional expectation method provided more accurate and precise predictions for two models developed from data with more observations per subject. For one model developed on data with fewer observations per subject, the first-order method provided better model predictions. All three models fitted by the first-order method produced some biologically unrealistic predictions, and the problem was more obvious on the data with fewer observations per subject. For all three models fitted by the first-order and first-order conditional expectation methods, the maximum likelihood and restricted maximum likelihood fits and the resulting model predictions were very close.

Crown width is an important predictor for tree growth, crown surface area, forest canopy cover, tree-crown profiles and wildlife habitat indices. This paper developed crown width models for white spruce (Picea glauca (Moench) Voss) in Alberta using allometric fixed and mixed models with varying degrees of model complexity. Diameter at breast height was the most important predictor and was used in the base model. Crown ratio, height-diameter ratio and two competition indices (CIs) were additional predictors added to the base model to form four expanded models. At each level of complexity, a fixed model and a mixed model were fitted. Improved fits were achieved for both model types as model complexity increased, and all mixed models provided much better fits than their fixed model counterparts. Population-averaged (PA) predictions by fixed models, and typical mean (TM), PA and plot-specific (PS) predictions by mixed models were compared on both model fitting and validation data. TM and PA predictions by each mixed model were almost identical, and they were less accurate than PA predictions by the fixed model counterpart, especially for simpler models. Much better PS predictions by mixed models were observed on both datasets. Although the distancedependent CI was slightly better than the distance-independent CI, both were not recommended due to their marginal contributions to crown width predictions.Keywords: crown width, mixed model, competition index, model prediction, white spruce RÉSUMÉ La largeur de cime est une variable importante pour estimer la croissance, la surface de cime, le couvert forestier, le profil de cime et les indices d'habitat pour la faune. Cet article propose un modèle de largeur de cime élaboré pour l' épinette blanche (Picea glauca (Moench) Voss) de l' Alberta à l'aide de modèles allométriques fixes et mixtes de divers niveaux de complexité. Le diamètre à hauteur de poitrine s' est avéré être la variable la plus importante et celle qui a été retenue dans le modèle de base. Le coefficient de forme, le rapport hauteur-diamètre et deux indices de compétition (CIs) ont été ajoutés au modèle de base afin de créer quatre modèles élargis. On a ajusté un modèle fixe et un modèle mixte pour chaque niveau de complexité. Dans les deux cas, l'ajustement du modèle s'améliorait à mesure qu'augmentait sa complexité, et les modèles mixtes donnaient un meilleur ajustement que les modèles fixes. On a comparé les prévisions moyennes avec celles au niveau des populations (Population-averaged -PA) obtenues avec les modèles fixes et les moyennes-types (TM), les prévisions PA et celles par placette (PS) obtenues avec les modèles mixtes à la fois sur leur ajustement et avec des ensembles de données de validation. Les prévisions TM et PA pour chacun des modèles mixtes ont été identiques et se sont avérées moins précises que les prévisions PA à l'aide des modèles fixes, surtout avec les modèles les plus simples. On a toutefois obtenu de bien meilleures prévisions PS avec les modèles mixtes lors de la validat...