Evaluation of parameter estimation methods for fitting spatial regression models

Abstract

Two types of spatial regression models, a spatial lag model (SLM) and a spatial error model (SEM), were applied to fit the height-diameter relationship of trees. SEM had better model fitting and performance than both SLM and ordinary least squares. Moran's I coefficients showed that SEM effectively reduced the spatial autocorrelation in the model residuals. Both real data and Monte Carlo simulations were used to compare different parameter estimation methods for the two spatial regression models, including maximum likelihood estimation (MLE), Bayesian methods, two-stage least squares (for SLM) and generalized method of moments (GMM) (for SEM). Our results indicated that GMM was close to MLE in terms of model fitting, much easier in computation, and robust to non-normality and outliers. The Bayesian method with heteroscedasticity did not effectively estimate the spatial autoregressive parameters but produced very small biases for the regression coefficients of the model when few outliers existed. © 2010 by the Society of American Foresters.