Two-Step Iterative GMM Structure for Estimating Mixed Correlation Coefficient Matrix

TL;DR

This paper introduces a novel two-step iterative GMM method for efficiently estimating mixed correlation matrices, offering consistency, asymptotic normality, and greater flexibility over traditional methods.

Contribution

The paper presents a new GMM-based approach for estimating mixed correlation matrices that is faster, flexible, and asymptotically as efficient as MLE, with improved initial estimation capabilities.

Findings

Estimation method is consistent and asymptotically normal.

Method is computationally faster than traditional approaches.

Flexible model setting allows for targeted coefficient estimation.

Abstract

In this article, we propose a new method for calculating the mixed correlation coefficient (Pearson, polyserial and polychoric) matrix and its covariance matrix based on the GMM framework. We build moment equations for each coefficient and align them together, then solve the system with Two-Step IGMM algorithm. Theory and simulation show that this estimation has consistency and asymptotic normality, and its efficiency is asymptotically equivalent to MLE. Moreover, it is much faster and the model setting is more flexible (the equations for each coefficient are blocked designed, you can only include the coefficients of interest instead of the entire correlation matrix), which can be a better initial estimation for structural equation model.