Network estimation of multi-dimensional binary variables with application to divorce data

Abstract

The cross-integration of statistics with social and scientific applications is one of the most popular topics in the past decade. Motivated by divorce data collected from the rural areas of Sichuan Province, China, we propose a new method to estimate the network of multiple binary variables, which specifies the dependence structures of multiple binary variables through the Gaussian copula model. Method of moments is employed to estimate the latent correlation matrix of the multiple binary variables. Alternating direction method of multipliers algorithm is then used to estimate the corresponding latent Gaussian network from the empirical latent correlation matrix. This method modifies the traditional estimation of latent Gaussian network from the perspectives of computational efficiency and positive definite guarantee. Analysis of the divorce data is conducted for illustration.