Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province, Southeast China

Abstract

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike’s information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R 2). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.

Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for Oaks (Quercus spp.) Considering Forest Structural Diversity

“…In order to check for multicollinearity amongst the variables, the variance inflation factor (VIF) was calculated. All variables with a VIF larger than 5 were removed to minimize overfitting [47,52,65]. Additionally, the relative importance refers to the quantification of an individual regressor's contribution to a multiple regression model.…”

“…Fixed effects parameters account for covariate or treatment effects as in traditional regression, while random effects parameters explain the different sources of stochastic variability [46][47][48]. Mixed-effects models are therefore extensively used in forestry, such as diameter-height models [49,50], crown models [51,52], self-thinning models [53][54][55], and growth models [56,57].…”

A Crown Width-Diameter Model for Natural Even-Aged Black Pine Forest Management

“…Very often, the field measurements that are obtained from established sample p hierarchical nested structure, which violates the basic least square assumption observations independence [32]. The mixed effect models provide an appropriate overcome this limitation [49] by estimating plot average parameters along with a rando is related specifically to each sample plot and, consequently, to the stand average co general vector form of a mixed effect model, with respect to crown width modeling, w as:…”

“…Very often, the field measurements t hierarchical nested structure, which vi observations independence [32]. The mix overcome this limitation [49] by estimating is related specifically to each sample plot general vector form of a mixed effect mod as:…”

“…Mixed-effect models of forest growth and yield have been recommended by several authors in the literature as an alternative solution to independency issues emanating from ordinary least squares application (e.g., [19,[21][22][23][24][25][26][27][28]). As far as crown width modeling is concerned, application of the mixed-effect modeling approach has been more limited as yet (Sánchez-González et al [23], Ducey [29], Fu et al [30,31], Hao et al [32], Yang and Huang [7] and Sharma et al [33,34]). In most cases, the mixed-effect models were reported to have generated more accurate predictions than the fixed effect models, since the structural heterogeneity, at tree or at stand level, was reflected by the random-effect parameters.…”