Abstract
In this study, we develop spatial autoregressive (SAR) models relating grizzly bear body length to environmental predictor variables in the Alberta Rocky Mountains. We examine the ability of several different spatial neighborhoods to model spatial dependence and compare the estimated parameters and residuals from a standard linear regression model (LRM) with those from three types of SAR models: error, lag, and Durbin. Further, we examine variable selection in the presence of negative dependence by repeating the modeling process using a SAR model. Two findings are that significant negative spatial dependence was present in the residuals of the LRM and that the choice of spatial neighborhood greatly affects the ability to detect spatial dependence. The incorporation of appropriate spatial weights into SAR models improves the fit and increases the significance of the parameter estimates vis-à-vis the linear model. The results of this study indicate that negative dependence may not have as severe negative effects on variable selection and parameter estimation as positive dependence. An examination of spatial dependence in regression modeling appears to be an important means of exploring the appropriateness of a sampling framework, predictor variables, and model form.
Citation
Timmins, T. L., Hunter, A. J. S., Cattet, M. R. L., & Stenhouse, G. B. (2013). Developing Spatial Weight Matrices for Incorporation into Multiple Linear Regression Models: An Example Using Grizzly Bear Body Size and Environmental Predictor Variables. Geographical Analysis, 45(4), 359–379. doi:10.1111/gean.12019