Simulation study for comparison of spatial autoregressive probit estimation methods

One of probit model variant with spatial dependent is spatial autoregressive (SAR) probit model. In SAR probit model, the spatial dependence structure adds complexity to the estimation of parameters. There are four methods for estimating the parameter of SAR probit model; maximum likelihood, Bayes, linearized GMM, and conditional approximate likelihood. The purpose of this article is to choose the best estimation method from four methods describes above using some extensive simulation which can handle sample sizes with large observations and various value of spatial lag coefficient, provided the spatial weight matrix is in an inconvenient sparse form, as is for large data sets, where each observation neighbors only a few other observations. The best estimation method is chosen based on the shortest confidence interval for the mean of SAR probit estimation, lowest bias, and Root Mean Square Errors (RMSE) of prediction. It was found that conditional approximate likelihood method was the best among the four methods concerning confidence interval and bias, yet regarding estimating RMSE, maximum likelihood estimation performed better. Maximum likelihood, Bayes, and conditional approximate likelihood method were better than linearized GMM in SAR probit parameter estimation for large dataset.