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Evaluation of Parameter Estimation Methods for Fitting Spatial Regression Models

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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.

Keywords: Bayesian methods; generalized method of moments; maximum likelihood estimation; spatial autoregressive parameters; tree height‚Äźdiameter relationship; two-stage least squares

Document Type: Research Article

Publication date: 2010-10-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
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