In this paper, we consider a spatial ordered probit model for analyzing spatial ordinal data with two or more ordered categories and, further, a spatial Tobit model for spatial proportional data with zero/one values. We develop a composite likelihood approach for parameter estimation and inference, which aims to balance statistical efficiency and computational efficiency for large datasets. The parameter estimates are obtained by maximizing a composite likelihood function via a quasi-Newton algorithm. The asymptotic properties of the maximum composite likelihood estimates are established under suitable regularity conditions. An estimate of the inverse of the Godambe information matrix is used for computing the standard errors, and the computation is further expedited by parallel computing. A simulation study is conducted to evaluate the performance of the proposed methods, followed by a real ecological data example. The connections between the spatial ordered probit model and the spatial Tobit model are explored using both simulated and real data.
