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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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.
Gunsjö, A. (1994).Faktoranalys av ordinala variabler. Doctoral dissertation. Uppsala University, Department of Statistics. (In Swedish)
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.
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.
Lee, S-Y., & Poon, W-Y. (1987). Two step estimation of multivariate polychoric correlation.Communications of Statistics—Theory and Methods, 16, 307–320.
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.
Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators.Psychometrika, 49, 115–132.
Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient.Psychometrika, 44, 443–460.
Parke, W. P. (1986). Pseudo maximum likelihood estimation: The asymptotic distribution.The Annals of Statistics, 14, 355–357.
Pierce, D. A. (1982). The asymptotic effect of substituting estimators for parameters in certain types of statistics.The Annals of Statistics, 10, 475–478.
Poon, W-Y., & Lee, S-Y. (1987). Maximum likelihood estimation of multivariate polychoric correlation coefficients.Psychometrika, 52, 409–430.
Author information
Authors and Affiliations
Additional information
The research was supported by the Swedish Council for Research in the Humanities and Social Sciences (HSFR) under the programMultivariate Statistical Analysis. The author thanks a reviewer for pointing out an error in the original version of the paper.
Rights and permissions
About this article
Cite this article
Jöreskog, K.G. On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika 59, 381–389 (1994). https://doi.org/10.1007/BF02296131
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02296131