Composite marginal likelihood estimation of spatial autoregressive probit models feasible in very large samples

Composite Marginal Likelihood (CML) has become a popular approach for estimating spatial probit models. However, for spatial autoregressive specifications the existing brute-force implementations are infeasible in large samples as they rely on inverting the high-dimensional precision matrix of the latent state variable. The contribution of this paper is to provide a CML implementation that circumvents inversion of that matrix and therefore can also be applied to very large sample sizes.