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

Abstract

An iteratively reweighted least squares (IRLS) method is proposed for the estimation of polyserial and polychoric correlation coefficients in this article. It calculates the slopes in a series of weighted linear regression models fitting on conditional expected values. For polyserial correlation, conditional expectations of the latent predictor is derived from the observed ordinal categorical variable, and the regression coefficient is obtained with the 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 the estimation of 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 computing speed. Supplementary materials for this article are available online.

Keywords:

• Iteratively reweighted least squares
• Linear regression
• Maximum likelihood
• Polychoric correlation
• Polyserial correlation
• Tetrachoric correlation

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge the Natural Science Foundation of Zhejiang Province (Project No. LDT23E05015A0, titled Isogeometric Analysis and Nonlinear Time Series Modeling of Error Field in Processing Domain of CNC Machine Tool).