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 principal criteria for determining the goodness of fit of forest models estimated by NLMM methods and for comparing alternative models and covariance structures. We also emphasized the importance of using pertinent graphic techniques to assess the appropriateness of NLMMs, especially at the subject-specific level, wherein lies the main interest of NLMMs.