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Re: st: Factor Analysis with ordinal and binary variables


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Factor Analysis with ordinal and binary variables
Date   Tue, 02 Jun 2009 16:04:51 -0400

On this issue,  the polyserial and polychoric correlations
can be used for binary and ordinal variables, respectively,
as input to a factor analysis, according to Joreskog and 
Sorbom, who did the research back in the 1980s.
    Bengt Muthen has also studied this matter.
Both teams have incorporated their findings into their
structural equation modeling packages.
      - Bob


Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

NSF grant:
http://www.colorado.edu/ibs/es/nuclear_disaster_risk/principal_investigators.html
Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Robert A Yaffee <bob.yaffee@nyu.edu>
Date: Tuesday, June 2, 2009 3:34 pm
Subject: Re: st: Factor Analysis with ordinal and binary variables
To: statalist@hsphsun2.harvard.edu


> Stefan,
>    Karl Joreskog and Dag Sorbom
> analyzed the problem back in the 1980s and found
> that you could use polyserial and polychoric correlations
> for a factor analysis of dichotomous or ordinal variables.
> If the ordinal variables have at least 15 levels they can
> be treated as continuous.
>     They have incorporated this finding in their program for
> structural equation modeling.
>     Regards,
>        Bob Yaffee
> 
> Bengt Muthen may have also written
> on this subject in the 1980s or early 1990s.
> 
> 
> Robert A. Yaffee, Ph.D.
> Research Professor
> Silver School of Social Work
> New York University
> 
> NSF grant:
> http://www.colorado.edu/ibs/es/nuclear_disaster_risk/principal_investigators.html
> Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf
> 
> CV:  http://homepages.nyu.edu/~ray1/vita.pdf
> 
> ----- Original Message -----
> From: "stefan.duke@gmail.com" <stefan.duke@gmail.com>
> Date: Tuesday, June 2, 2009 7:51 am
> Subject: st: Factor Analysis with ordinal and binary variables
> To: statalist@hsphsun2.harvard.edu
> 
> 
> > Hello,
> > 
> > I have question concerning factor analysis on variables with different
> > measurement levels.
> > 
> > The questionnaire consists of binary and ordinal variables. If I would
> > have just binary variables, I would use the tetrachoric correlation
> > coefficients. For the ordinal I assume approx. normality and then use
> > the ordinary factor analysis capability.
> > 
> > But what do I do when I have both variables? Is it an option to
> > construct the variance-covariance matrix by  hand? And what do I take
> > for the correlation between binary and ordinal?
> > 
> > Maybe is there a model class which takes care of that, that yields
> > similar outcomes as factor analysis but can deal with such kind of
> > data (e.g. correspondence analysis).
> > 
> > I am grateful for every hint.
> > 
> > Best,
> > Stefan
> > *
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