Hostname: page-component-5f745c7db-nzk4m Total loading time: 0 Render date: 2025-01-06T07:08:35.850Z Has data issue: true hasContentIssue false
  • English
  • Français

Testing the Assumptions Underlying Tetrachoric Correlations

Published online by Cambridge University Press:  01 January 2025

Bengt Muthén  and
Charles Hofacker
Bengt Muthén*
Affiliation:
Graduate School of Education, University of California, Los Angeles
Charles Hofacker
Affiliation:
College of Business and Marketing, Florida State University
*
Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, Los Angeles, CA 90024.
Get access Rights & Permissions [Opens in a new window]

Abstract

A method is proposed for empirically testing the appropriateness of using tetrachoric correlations for a set of dichotomous variables. Trivariate marginal information is used to get a set of one-degree of freedom chi-square tests of the underlying normality. It is argued that such tests should preferrably preceed further modeling of tetrachorics, for example, modeling by factor analysis. The assumptions are tested in some real and simulated data.

Keywords

normalitydichotomous variablesLISCOMPfactor analysis
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 4 , December 1988 , pp. 563 - 577
Copyright
Copyright © 1988 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

Presented at the Psychometric Society meeting in Santa Barbara, California, June 25–26, 1984. The research of the first author was supported by Grant No. SES-8312583 from the National Science Foundation.

References

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Bock, R. D., & Lieberman, M. (1970). Fitting a response model forn dichotomously scored items. Psychometrika, 35, 179–197.CrossRefGoogle Scholar
Brown, M. B., & Benedetti, J. K. (1977). On the mean and variance of the tetrachoric correlation coefficient. Psychometrika, 42, 347–355.CrossRefGoogle Scholar
Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5–32.CrossRefGoogle Scholar
Divgi, D. R. (1979). Calculation of the tetrachoric correlation coefficient. Psychometrika, 44, 169–172.CrossRefGoogle Scholar
Kendall, M., & Stuart, A. (1979). The advanced theory of statistics (Vol. 2), New York: McMillan.Google Scholar
Kirk, D. B. (1973). On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient. Psychometrika, 38, 259–268.CrossRefGoogle Scholar
Muthén, B. (1978). Contributions to factor analysis of dichotomous dependent variables. Psychometrika, 43, 551–560.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
Muthén, B. (1987). LISCOMP. Analysis of linear structural equations with a comprehensive measurement model. User's guide, Mooresville, IN: Scientific Software.Google Scholar
Muthén, B., & Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46, 407–419.CrossRefGoogle Scholar
Pearson, K., & Heron, D. (1913). On theories of association. Biometrika, 9, 159–315.CrossRefGoogle Scholar
Vaswani, S. (1950). Assumptions underlying the use of the tetrachoric correlation coefficient. Sankhya, 10, 269–276.Google Scholar
Yule, G. U. (1912). On the methods of measuring association between two attributes. Journal of the Royal Statistical Society, 75, 579–652.CrossRefGoogle Scholar