Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients

An iteratively reweighted least squares (IRLS) method is proposed for the estimation of polyserial and polychoric correlation coefficients in this paper. It calculates slopes a series weighted linear regression models fitting on conditional expected values. For correlation, expectations latent predictor derived from observed ordinal categorical variable, coefficient obtained with method. In estimating coefficient, response variable are updated turns. Standard errors estimators using delta based data summaries instead whole data. Conditional univariate normal distribution exploited single integral numerically evaluated algorithm, comparing to double computed bivariate traditional maximum likelihood (ML) approaches. This renders new algorithm very fast both coefficients. Thorough simulation studies conducted compare performances classical ML methods. Real analyses illustrate advantage computing speed.