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Article #1244Factor analysis of dichotomous variables
From: Andrew Mackinnon
Date: Fri, 02 Jul 1993 06:57
Date: Fri, 02 Jul 1993 06:57
63 lines
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3374 bytes
The recent discussion about the factor analysis dichotomous variables doesn't really seem to have taken on board the recent literature on the subject. I've been looking at the literature on the subject for my own work. Here are some other views. McDonald (1985) has an insightful approach to this problem. If you view factor analysis as a regression of a latent variable onto observed variables, the potential problems are clarified a little. The question is less one of what coefficients are appropriate and more one of whether a linear relationship between the continuous latent variable and the dichotomous observed variable is appropriate. Strictly it cannot be: the dichotomy is bounded by 0,1 and the regression may predict values outside this range. This suggests that a non-linear relation between the factor and observed variables should be modelled. This is, essentially what a lot of latent trait or item response models do. So the question about factor analysis and dichotomies might be better considered as what sort of formal model is being applied to the data rather than a "coefficient war". Of course, in practise, the linear regression of ordinary factor analysis may work quite well: so long as the dichotomies don't involve extreme proportions (for example 5/95%), a linear relationship will be quite close to, say, a logistic one. This has been demonstrated in McDonald, R.P. & Ahlawat, K.S. (1974). Whether more sophisticated methods of analysis are better than the analysis of ordinary correlations of binary variables (phi coefficients) was also investigated by Parry & McArdle (1991). Their simulation experiment failed to demonstrate the overall superiority of these methods, but of course, it is easy to construct data structures where this would not be the case. Some useful references: McDonald. R.P. (1985) Factor analysis and related methods. LEA: Hillsdale, N.J. McDonald, R.P. and Ahlawat, K.S. (1974) Difficulty factors in binary data. British Journal of Mathematical and Statistical Psychology, 1974, 27, 82-99. Parry, C.D.H., & McArdle, J.J. (1991) An applied comparison of methods for least-squares factor analysis of dechotomous variables. Applied Psychological Measurement, 15, 35-45. --------------------------------------------------------------------- Andrew Mackinnon Fax: +61 6 249 0733 Social Psychiatry Research Unit Tel: +61 6 249 2741 Australian National University Email: Andrew.Mackinnon@anu.edu.au Canberra ACT 0200 Australia ---------------------------------------------------------------------
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f5efb,348eb23daa35e368,start X-Google-Attributes: gidf5efb,public X-Google-ArrivalTime: 1993-07-02 00:04:11 PST Path: arc1-ca.pugleaf.net!gmd.de!newsserver.jvnc.net!howland.reston.ans.net!spool.mu.edu!uunet!munnari.oz.au!newshost.anu.edu.au!newsmaster From: Andrew Mackinnon <Andrew.Mackinnon@anu.edu.au> Newsgroups: bit.listserv.stat-l Subject: Factor analysis of dichotomous variables Date: 2 Jul 1993 06:57:16 GMT Organization: Social Psychiatry, ANU Lines: 63 Distribution: world Message-ID: <210m8c$1t7@manuel.anu.edu.au> NNTP-Posting-Host: 150.203.101.131 X-UserAgent: Nuntius v1.1.1d11 X-XXDate: Fri, 2 Jul 93 17:00:40 GMT