One problem with doing traditional factor analyses on dichotomous variables is that unless the dichotomous variables have means around .5, they can seriously underestimate the true degree of correlation. Some recommend using tetrachoric correlations to get around this but such correlations may lead to matrices with negative eigenvalues.
I tend to agree with Dale that it's often better to use a tool specifically designed to handle the problem. That's why I recommend Mplus for such analyses.
Paul
Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of Hector Maletta
Sent: Wednesday, January 13, 2010 5:29 PM
To:
[hidden email]Subject: Re: Factor Analysis on dichotomous variables
Any factor analysis can be run on dichotomous variables, because these
variables can legitimately be considered as interval measures. As only one
interval is involved (from 0 to 1),
there is no question of comparing
unequal intervals. Their mean is the proportion (p) of the value 1, and the
variance is p(1-p).
There is a specific SPSS procedure, CATPCA, for principal component analysis
of categorical variables (ordinal or nominal, any number of categories)..
However, for dichotomous variables CATPCA gives the same solution as
classical Principal Components Analysis of interval variables (PCA is one of
the variants of factor analysis).
Purists insist that dichotomous variables cannot be used in anything related
to regression, because their residuals are not normally distributed. To see
this, one has to see that the predicted value for a dichotomous variable is
either a value between 0 and 1, or a value outside that interval. In the
first case, the actual values will be either 1 or 0, and the residuals would
therefore be piled at the ends of the 0,1 interval, and not around the
predicted
value. In the second case, the residuals will all be at one side
of the predicted value. In any case, their distribution would not be normal.
However, dummy variables (i.e. variables with value 0 or 1) are routinely
used in regression. Factor analysis is a variant of linear regression (or,
more widely, a variant of the Generalized Linear Model) and therefore this
habitual use applies also to it.
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
SPSSX-L@LISTSERV..UGA.EDU] On Behalf Of
Angelina S. MacKewn
Sent: 13 January 2010 19:41
To:
[hidden email]Subject: Factor Analysis on dichotomous variables
What is the factor analysis (PCA) equivalent that can be run on dichotomous
variables. I have 50
exhibited behaviours (yes/no) that I want to factor
together. I have a sample size of about 500. I would be using SPSS and could
use syntax if it is available.
Thanks,
Angie
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