Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

Abstract

An individual-tree diameter growth model was developed for Cunninghamia lanceolata in Fujian province, southeast China. Data were obtained from 72 plantation-grown China-fir trees in 24 single-species plots. Ordinary non-linear least squares regression was used to choose the best base model from among 5 theoretical growth equations; selection criteria were the smallest absolute mean residual and root mean square error and the largest adjusted coefficient of determination. To account for autocorrelation in the repeated-measures data, we developed one-level and nested two-level nonlinear mixed-effects (NLME) models, constructed on the selected base model; the NLME models incorporated random effects of the tree and plot. The best random-effects combinations for the NLME models were identified by Akaike's information criterion, Bayesian information criterion and −2 logarithm likelihood. Heteroscedasticity was reduced with two residual variance functions, a power function and an exponential function. The autocorrelation was addressed with three residual autocorrelation structures: a first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and a compound symmetry structure (CS). The one-level (tree) NLME model performed best. Independent validation data were used to test the performance of the models and to demonstrate the advantage of calibrating the NLME models.

Above- and belowground tree biomass models for three mangrove species in Tanzania: a nonlinear mixed effects modelling approach

“…This supports the role of random effects in explaining unexplained sources of variation which is only possible within the mixed modelling framework. In line with our results, Chave et al (2005) reported that the inclusion of ht into a common mangrove biomass model reduced the standard error of aboveground biomass from 19.5 to 12.5 % for mangrove trees, while other authors reported that random effects improved predictive power of biomass models for non-mangrove trees (e.g., Fu et al 2014;Xu et al 2014). …”

“…Biomass models based on mixed effects modelling frameworks have also previously been developed (e.g., Moore 2010;Li et al 2011;Xu et al 2014). The mixed effects modelling provides a statistical capability where fixed-(i.e., populations average) and random effects (i.e., group specific) parameters may be estimated simultaneously (West et al 2007).…”

“…The mixed effects modelling provides a statistical capability where fixed-(i.e., populations average) and random effects (i.e., group specific) parameters may be estimated simultaneously (West et al 2007). Under the mixed effects modelling framework, models including fixed effects parameters may therefore be regarded as common or multi-species models, while those including random effects may be regarded as species-specific models.…”

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

“…Mathematical technique of a system of uniform diameter and height regional functions is the approach known as the generalized model. The mixed effects regression models are able to achieve the same results than the generalized model [10, 33]. In this study new developed mixed effects parameters height-diameter relationships demonstrated similar statistical indexes as in the nonlinear generalized height-diameter regression models presented by Petrauskas et al [34].…”

“…Mixed effects models allow fixed and random parameters to be estimated simultaneously and evaluate the value of the random parameters for a location not present in the original estimation dataset. This approach is known as calibration and can be applied if a sub-sample of trees measured for the total height and breast height diameter are available [10]. Fixed effects parameter SDEs are used in a wide range of applications in environmental, engineering, and biological modeling [11–14].…”