🚀 go-pugleaf

RetroBBS NetNews Server

Inspired by RockSolid Light RIP Retro Guy

Article View: bit.listserv.stat-l
Article #1244

Factor analysis of dichotomous variables

#1244
From: Andrew Mackinnon
Date: Fri, 02 Jul 1993 06:57
63 lines
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
---------------------------------------------------------------------
Technical Details
Message-ID: <210m8c$1t7@manuel.anu.edu.au>
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

Show Full Headers
Complete Article Headers
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