Modeling and prediction of tree height-diameter relationships using spatial autoregressive models

Abstract

Three spatial autoregressive models were applied to model the tree height- diameter relationship, including spatial lag model (SLM), spatial error model (SEM), and spatial Durbin model (SDM), with ordinary least squares (OLS) as a benchmark. Five spatial weight matrices were used to evaluate the impacts of different weighting schemes on model fitting. It was evident that different schemes of spatial weight matrix strongly affected the model fitting and parameter estimation in these spatial autoregressive models. We found that the variogram or geostatistical weight matrix was superior to other spatial weight matrices such as contiguity, inverse distances, and local Gi* statistics. Further, the spatial autoregressive models were used to predict tree heights at unsampled locations. The results showed that the three spatial autoregressive models overperformed the OLS model not only in model fitting and reducing spatial dependence, but also in model predictions. In general, SDM and SEM performed significantly better than SLM, whereas SDM was slightly better than SEM in each aspect of model fitting and prediction. However, if the complexity of the model structure is a concern, SEM with a geostatistical weight matrix is a reasonable choice over SDM because SEM offers the model coefficient estimates close to those of the OLS model, which makes the interpretation and understanding of the model much easier. © 2011 by the Society of American Foresters.