  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.
