EM algorithm in Gaussian copula with missing data

Rank-based correlation is widely used to measure dependence between variables when their marginal distributions are skewed. Estimation of such correlation is challenged by both the presence of missing data and the need for adjusting for confounding factors. In this paper, we consider a unified framework of Gaussian copula regression that enables us to estimate either Pearson correlation or rank-based correlation (e.g. Kendall's tau or Spearman's rho), depending on the types of marginal distributions. To adjust for confounding covariates, we utilize marginal regression models with univariate location-scale family distributions. We establish the EM algorithm for estimation of both correlation and regression parameters with missing values. For implementation, we propose an effective peeling procedure to carry out iterations required by the EM algorithm. We compare the performance of the EM algorithm method to the traditional multiple imputation approach through simulation studies. For structured types of correlations, such as exchangeable or first-order auto-regressive (AR-1) correlation, the EM algorithm outperforms the multiple imputation approach in terms of both estimation bias and efficiency.