Testing the Assumptions Underlying Tetrachoric Correlations

Bengt Muthén · Charles F. Hofacker

70 citations0/0 files storedPsychometrika

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Psychometric Methodologies and Testing Statistical Methods and Applications Statistical Methods and Bayesian Inference

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.

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References

1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1984A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators 1970Fitting a Response Model for n Dichotomously Scored Items 1978Contributions to Factor Analysis of Dichotomous Variables 1975Factor Analysis of Dichotomized Variables 1981Simultaneous Factor Analysis of Dichotomous Variables in Several Groups 1979Calculation of the Tetrachoric Correlation Coefficient 1977On the Mean and Variance of the Tetrachoric Correlation Coefficient

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