In recent years, spatial data widely exist in various fields such as finance, geology, environment, and natural science. These data collected by many scholars often have geographical characteristics. The spatial autoregressive model is a general method to describe the spatial correlations among observation units in spatial econometrics. The spatial logistic autoregressive model augments the conventional logistic regression model with an extra network structure when the spatial response variables are discrete, which enhances classification precision. In many application fields, prior knowledge can be formulated as constraints on the parameters to improve the effectiveness of variable selection and estimation. This paper proposes a variable selection method with linear constraints for the high-dimensional spatial logistic autoregressive model in order to integrate the prior information into the model selection. Monte Carlo experiments are provided to analyze the performance of our proposed method under finite samples. The results show that the method can effectively screen out insignificant variables and give the corresponding coefficient estimates of significant variables simultaneously. As an empirical illustration, we apply our method to land area data.

When the spatial response variables are discrete, the spatial logistic autoregressive model adds an additional network structure to the ordinary logistic regression model to improve the classification accuracy. With the emergence of high-dimensional data in various fields, sparse spatial logistic regression models have attracted a great deal of interest from researchers. For the high-dimensional spatial logistic autoregressive model, in this paper, we propose a variable selection method with for the spatial logistic model. To identify important variables and make predictions, one efficient algorithm is employed to solve the penalized likelihood function. Simulations and a real example show that our methods perform well in a limited sample.