A J-test for spatial autoregressive binary models

Spatial autoregressive binary models are well established in spatial statistics and econometric literature. Recently, different estimation methods have been proposed that account for logistic as well as probit regressions. In spatial models the choice of the spatial weighting matrix is crucial to reflect the amount of correlation in the data. This article proposes a simple $J$-test procedure for spatial autoregressive binary model. Since the $J$-test is a non-nested test, it can be used, among other things, to test the specification of the spatial weighting matrix. The $J$-test is based on augmenting the null model with the predictor from the alternative model(s). After defining these predictors, we develop the theory and derive the steps for the $J$-test. We also evaluate the finite sample properties in the context of a Monte Carlo experiment. An empirical application on firms’ decisions to reopen in the aftermath of Hurricane Katrina for New Orleans is also presented.