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

TL;DR: In this article , an iteratively reweighted least squares (IRLS) method is proposed for estimating polyserial and polychoric correlation coefficients, which iteratively calculates the slopes in a series of weighted linear regression models based on conditional expected values.

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