Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2025-01-05T16:15:02.842Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Estimation of Polychoric Correlations and their Asymptotic Covariance Matrix

Published online by Cambridge University Press:  01 January 2025

Karl G. Jöreskog
Karl G. Jöreskog*
Affiliation:
Uppsala University
*
Requests for reprints should be sent to Karl G. Jöreskog, Department of Statistics, Uppsala University, PO Box 513, S-75120 Uppsala, SWEDEN.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general theory for parametric inference in contingency tables is outlined. Estimation of polychoric correlations is seen as a special case of this theory. The asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds. Computational aspects are also discussed.

Keywords

ordinal variablespolychoric correlationsmaximum likelihoodasymptotic covariance matrix
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 3 , September 1994 , pp. 381 - 389
Copyright
Copyright © 1994 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The research was supported by the Swedish Council for Research in the Humanities and Social Sciences (HSFR) under the program Multivariate Statistical Analysis. The author thanks a reviewer for pointing out an error in the original version of the paper.

References

Aish, A. M., Jöreskog, K. G. (1990). A panel model for political efficacy and responsiveness: An application of LISREL7 with weighted least squares. Quality and Quantity, 24, 405–426.CrossRefGoogle Scholar
Gunsjö, A. (1994). Faktoranalys av ordinala variabler. Doctoral dissertation. Uppsala University, Department of Statistics. (In Swedish)Google Scholar
Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387–404.CrossRefGoogle Scholar
Jöreskog, K. G., Sörbom, D. (1988). PRELIS-A program for multivariate data screening and data summarization. A preprocessor for LISREL 2nd ed.,, Chicago, IL: Scientific Software.Google Scholar
Lee, S-Y., Poon, W-Y. (1987). Two step estimation of multivariate polychoric correlation. Communications of Statistics—Theory and Methods, 16, 307–320.CrossRefGoogle Scholar
Lee, S-Y., Poon, W-Y., Bentler, P. M. (1990). A three-stage estimation procedure for structural equation models with polytomous variables. Psychometrika, 55, 45–51.CrossRefGoogle Scholar
Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132.CrossRefGoogle Scholar
Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443–460.CrossRefGoogle Scholar
Parke, W. P. (1986). Pseudo maximum likelihood estimation: The asymptotic distribution. The Annals of Statistics, 14, 355–357.CrossRefGoogle Scholar
Pierce, D. A. (1982). The asymptotic effect of substituting estimators for parameters in certain types of statistics. The Annals of Statistics, 10, 475–478.CrossRefGoogle Scholar
Poon, W-Y., Lee, S-Y. (1987). Maximum likelihood estimation of multivariate polychoric correlation coefficients. Psychometrika, 52, 409–430.CrossRefGoogle Scholar