An individual height-diameter model constructed using spatial autoregressive models within natural spruce-fir and broadleaf mixed stands.

Spatial autocorrelation is a common phenomenon in forestry. It directly connects competition and interaction among individuals. Individual height-diameter models are fundamentally important for forest growth, yield modeling and forecasting. Violation of residual independent distribution assumption in ordinary least squares (OLS) will inflate type 1 errors, lead to biased estimates of the standard errors of model parameters, and decrease the efficiency of estimation in a regression model, if the spatial autocorrelation among the individuals is ignored. Therefore, three simultaneous autoregressive (SAR) models, including spatial lag model (SLM), spatial error model (SEM) and spatial Durbin model (SDM) within five spatial weight matrices, including Delaunay triangulation (DT), inverse distance raised to one power (ID1), inverse distance raised to two powers (ID2), inverse distance raised to five powers (ID5) and Gaussian variogram (GV), were applied to construct individual height-diameter models of natural spruce-fir and broadleaf mixed stands which are the main forest type in northeast China, with linearization individual height-diameter OLS model as a benchmark model. Model parameters of three SAR models were estimated by maximum likelihood. Model coefficients of OLS and three SAR models were tested by t-test, the autoregressive parameters of three SAR models were all tested by likelihood ratio test. Morans I (MI) was selected to compare autocorrelation of four model residuals. Three statistical indices, i.e. coefficient of determination (R2), root mean square error (RMSE) and Akaike information criterion (AIC), were regarded as the appropriate criteria to identify the model fitting among OLS, SLM, SDM and SEM. Mean square error (MS) was selected to identify the predictive validity among four models. Results show that residuals of OLS were positive spatial dependence for ignoring the spatial autocorrelation among individuals. The model fittings of three SAR models were better than that of OLS. Among the three SAR models, model fitting of SLM was worse than those of SDM and SEM. SLM do not remove but reduce the spatial autocorrelation of model residuals, and slightly improve the model fitting, no matter which spatial weight matrices are used in SLM. All of the spatial weight matrices used in SDM and SEM could remove the spatial autocorrelation of residuals; however, GV was only applicable to SEM. Among all spatial weight matrices, ID2 was the best spatial weight matrix. Using ID2 into four modes, the predictive validity of SDM and SEM was superior to that of SLM, while the predictive validity of three SAR was better than that of OLS. Using three SAR models, fitting and prediction of individual diameter at breast height and height models were improved, and it may provide a theoretical basis for reasonable management of natural spruce-fir and broadleaf mixed stands.