Testing the Assumptions Underlying Tetrachoric Correlations

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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.