Efficient and feasible inference for high-dimensional normal copula regression models

TL;DR

This paper introduces a weighted composite likelihood approach for high-dimensional normal copula regression models, significantly improving estimation efficiency for discrete responses compared to traditional methods.

Contribution

It proposes a novel weighted composite likelihood method with an iterative scheme to enhance estimation efficiency in high-dimensional MVN copula models with discrete data.

Findings

Nearly as efficient as maximum likelihood estimation.

Substantial efficiency gains over unweighted composite likelihood.

Effective in both simulation and real data applications.

Abstract

The composite likelihood (CL) is amongst the computational methods used for the estimation of high-dimensional multivariate normal (MVN) copula models with discrete responses. Its computational advantage, as a surrogate likelihood method, is that is based on the independence likelihood for the univariate regression and non-regression parameters and pairwise likelihood for the correlation parameters, but the efficiency of estimating the univariate regression and non-regression parameters can be low. For a high-dimensional discrete response, we propose weighted versions of the composite likelihood estimating equations and an iterative approach to determine good weight matrices. The general methodology is applied to the MVN copula with univariate ordinal regressions as the marginals. Efficiency calculations show that our method is nearly as efficient as the maximum likelihood for fully specified MVN copula models. Illustrations include simulations and real data applications regarding longitudinal (low-dimensional) and time (high-dimensional) series ordinal response data with covariates and it is shown that there is a substantial gain in efficiency via the weighted CL method.