Shawn X. Meng

Assessing the goodness of fit of forest models estimated by nonlinear mixed-model methods

In this study we examined various measures, including the concordance correlation (CC) coefficient, for determining the goodness of fit of forest models estimated by nonlinear mixed-model (NLMM) methods. Based on the volume–age data for black spruce, we analyzed the use of CC and other traditional goodness-of-fit measures such as coefficient of determination (R2), mean bias, percent bias, root mean square error, and graphic techniques on both the population and subject-specific levels within the NLMM framework. We also examined the relationship between goodness-of-fit measures and the number of observations per subject. We found that the standard overall goodness-of-fit measures commonly reported on combined data from different subjects were generally insufficient in determining the goodness of fitted models. We recommend that CC and other selected goodness-of-fit measures be calculated for individual subjects, and that the frequency distributions of the calculated values be examined and used as the princ...

A multilevel individual tree basal area increment model for aspen in boreal mixedwood stands

Based on a multilevel nonlinear mixed model approach, a basal area increment model was developed for individual aspen (Populus tremuloides Michx.) trees growing in boreal mixedwood stands in Alberta. Various stand and tree characteristics were evaluated for their contributions to model improvement. Total stand basal area, basal area of larger trees, and the ratio of target tree height to maximum stand height were found to be significant predictors. When random effects were modeled at the plot level alone, correlations among normalized residuals remained significant. These correlations were successfully removed when random effects were modeled at both plot and tree levels. The predictive abilities of two alternative models were evaluated at the population, plot, and tree levels. At the tree level, a tree measured at the first growth period was used for estimating random parameters, and basal area increments of that tree in future growth periods were subsequently predicted. At the plot level, one to five tr...

Evaluation of population-averaged and subject-specific approaches for modeling the dominant or codominant height of lodgepole pine trees.

Population-averaged (PA) and subject-specific (SS) approaches for modeling the height of dominant or codominant lodgepole pine (Pinus contorta Dougl. ex Loud.) trees were evaluated using six candidate models derived from the Chapman–Richards and logistic functions. The true PA response obtained from separate fits of the models was compared with the typical mean (TM) response computed using only the fixed-effects parameters of the mixed-effects models. Results showed that the TM response had higher prediction errors than the PA response, suggesting that a true PA response and not the TM response is needed to reflect the overall mean response of the model. The SS approach produced improved height predictions relative to the PA approach when evaluated using independent validation data. In addition, the logistic performed better than the Chapman–Richards function, regardless of whether the SS or PA approach was applied. Among the candidate models, the logistic function with the inclusion of site index gave th...

Incorporating correlated error structures into mixed forest growth models: prediction and inference implications.

Three nonlinear mixed models with and without incorporating a function to model the serial correlation were compared with regard to their predictive abilities. Results showed that accounting for the serial correlation using the spatial power (SP(POW)) or Toeplitz (TOEP(X)) functions resulted in a large reduction in serial correlation and improved the fit of the models. The improved model fits, however, did not unanimously translate into improved model predictions when evaluated under different scenarios. In many cases, the models with the simple independent and identically distributed structure outperformed the models with the SP(POW) or TOEP(X) structure in terms of the models’ predictive ability. We also examined the effect of adjusting predictions based on the prediction theorem within the nonlinear mixed modeling framework. It was shown that, in general, the adjusted predictions had lower errors than those without adjustment, but the differences were small in many cases. The adjustment with three prio...