Testing Significance of Tetrachoric Correlation Coefficient Matrix of Binary Variables

The tetrachoric correlation coefficient is often used in a 2x2 contingency table to measure the relationship of two binary variables assuming that each variable has an underlying continuous normal distribution. Researchers often demand a correlation matrix of more than two variables to perform more advanced statistical techniques such as multivariate analysis, factor analysis, or structural equation modeling. However, most software lacks the ability to do so. We implemented a program to achieve the goal. The algorithm used Divgi's method as starting values, and exercised tetrachoric series expansion and Gaussian quadrature with a 32-point quadrature adjustment to avoid possibly infinite number of iterations. The program also takes sparse and negative frequencies into consideration. We discussed the algorithm calculating the tetrachoric correlation coefficient matrix and their asymptotic standard errors. The program also performs hypothesis testing for significance of tetrachoric correlation coefficients.