Interpreting spatial regression models with multiplicative interaction explanatory variables

Abstract

Use of multiplicative interaction of explanatory variables has been a standard practice in the regression modeling literature, and estimation of the parameters of such a model in the case of spatial autoregressive (SAR) or spatial Durbin (SDM) models can be accomplished using existing software for spatial regression estimation. However, use of the conventional scalar summary estimates of direct and indirect effects reflecting the own- and other-region impacts on the dependent variable associated with changes in the explanatory variables will not produce valid inferences. We discuss the issues that arise and introduce new methods for interpretation of own- and other-region impacts based on estimates from this type of model.