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• W2765698172 abstract "PSYCHOMETR1KA--VOL. 53, NO. 4, 563--578 DECEMBER 1988 TESTING THE ASSUMPTIONS UNDERLYING TETRACHORIC CORRELATIONS BENGTMUTH~N GRADUATE SCHOOL OF EDUCATION UNIVERSITY OF CALIFORNIA, LOS ANGELES CHARLES HOFACKER COLLEGE OF BUSINESS AND MARKETING FLORIDA STATE UNIVERSITY A method is proposed for empirically testing the appropriateness of using tetrachoric corre- lations 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. Key words: normality, dichotomous variables, LISCOMP, factor analysis. Introduction Recent discussions of the t e t r a c h o r i c c o r r e l a t i o n coefficient include the topics o f i m p r o v e d efficiency a n d a c c u r a c y of c o m p u t a t i o n (see e.g., Divgi, 1979; K i r k , 1973), the statistical p r o p e r t i e s of the e s t i m a t e a n d its s t a n d a r d e r r o r (Brown & Benedetti, 1977), a n d the fitting of factor analysis m o d e l s to tetrachorics (see e.g., Bock & L i e b e r m a n , 1970; Christoffersson, 1975; M u t h e n , 1984; M u t h 6 n & Christoffersson, 1981). T h e a p p r o p r i - ateness of using the t e t r a c h o r i c c o r r e l a t i o n coefficient, however, has n o t been given recent attention. T h e t e t r a c h o r i c assumes b i v a r i a t e n o r m a l i t y for c o n t i n u o u s latent response variables u n d e r l y i n g a p a i r of d i c h o t o m o u s measures. T o d a y ' s t e x t b o o k t r e a t m e n t of coefficients of a s s o c i a t i o n for d i c h o t o m o u s variables offers r a t h e r vague g u i d a n c e a b o u t the realism of this. Little c o n c i l i a t i o n seems to have been r e a c h e d since the h e a t e d t u r n of the c e n t u r y d e b a t e between P e a r s o n a n d Yule, where in a r g u i n g for c o n s i d e r i n g o n l y the o b s e r v e d variables, Yule r e m a r k e d (1912): ... all those w h o have died of s m a l l p o x are equally d e a d : no one is m o r e d e a d o r less d e a d t h a n a n o t h e r , a n d the d e a d are quite distinct from the survivors (pp. with the familiar response: ... if Mr. Yule's views are accepted, i r r e p a r a b l e d a m a g e will be d o n e to the g r o w t h of m o d e r n statistical t h e o r y ( P e a r s o n & H e r o n , 1913, p. 159). This p a p e r builds on the view t h a t the a p p r o p r i a t e n e s s of tetrachorics need n o t be a p h i l o s o p h i c a l m a t t e r but one of statistical inference. T h e r e is a h y p o t h e s i s o f u n d e r l y i n g Requests for reprints should be sent to Bengt Muth6n, Graduate School of Education, University of California, Los Angeles, Los Angeles, CA 90024. Presented at the Psychometric Society meeting in Santa Barbara, California, June 25-26, 1984. The re- search of the first author was supported by Grant No. SES-8312583 from the National Science Foundation. © 1988 The Psychometric Society" @default.
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• W2765698172 title "Testing the Assumptions Underlying Tetrachoric Correlations - eScholarship" @default.
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