Geographically Local Linear Mixed Models for Tree Height-Diameter Relationship

Abstract

A geographically local linear mixed model (GLLMM) was proposed to handle spatial autocorrelation and heterogeneity simultaneously. Under the framework of geographically weight regression (GWR), GLLMM incorporated the spatial dependence among neighboring observations at each location in the study area by modeling local variograms and using spatial weighting matrix. Our results indicated that GLLMM fitted the example data better than GWR as measured by the Akaike information criterion for appropriate bandwidths. We also tested the ability of GWR and GLLMM in spatial interpolation using a subset of data. GLLMM had higher prediction accuracy and smaller spatial autocorrelation in model residuals than did GWR. Further, GLLMM enabled mapping of the geostatistical parameters of local variograms, which were used to identify spots or local areas of high spatial heterogeneity or autocorrelation in the study region. Therefore, GLLMM is a useful local regression technique for modeling the variable relationships in forest stands with heterogeneous micro-site conditions and diverse correlations between neighboring trees.