Maximum likelihood estimation of the polychoric correlation coefficient

The polychoric correlation is discussed as a generalization of the tetrachoric correlation coefficient to more than two classes. Two estimation methods are discussed: Maximum likelihood estimation, and what may be called two-step maximum likelihood estimation. For the latter method, the thresholds are estimated in the first step. For both methods, asymptotic covariance matrices for estimates are derived, and the methods are illustrated and compared with artificial and real data.This paper was read at the 1978 European Meeting on Psychometrics and Mathematical Psychology in Uppsala, Sweden, June 1978.Research reported in this paper has been supported by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog.