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RE: st: Factor Analysis with ordinal and binary variables


From   jverkuilen <jverkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Factor Analysis with ordinal and binary variables
Date   Thu, 4 Jun 2009 11:04:44 -0400

The program Mplus by Bengt Muthen is set up on the explicit principle of mixed measurement levels. Michael Neale's free MX can also do what you want and I am sure there are R packages that will, possibly LTM by Demetrios Rizopoulous. 

In Stata, -gllamm- could do what you want for a confirmatory model. 

For an exploratory model in Stata, using -factormat- on polychoric correlations seems your best bet, though sadly it doesn't have standard errors for loadings. Essentially this is what Mplus and other programs do anyway (with some refinements and bells and whistles).  

Joint correspondence analysis found in Stata under -mca- is an alternative that is an analog of MINRES/least squares factor analysis for nominal data based on minimizing a chi squared loss function through alternating least squares.  

Finally, you could consider a log-multiplicative association model, which is a maximum likelihood version of factor analysis for nominal variables that greatly elaborates Leo Goodman's RC association model. LatentGOLD and the free LEM by Jeroen Vermunt (the former with Jay Magidson) will fit these. See the 2000 paper by Carolyn Anderson and Vermunt in Sociological Methodology and subsequent publications by Anderson, Vermunt, and colleagues (including yours truly). These models end up being constrained Poisson regressions and could be ported to Stata easily enough.   

-----Original Message-----
From: "stefan.duke@gmail.com" <stefan.duke@gmail.com>
To: statalist@hsphsun2.harvard.edu
Sent: 6/3/2009 6:12 AM
Subject: Re: st: Factor Analysis with ordinal and binary variables

Hi ya'll,
thanks for you advice, so I know now where to look.
Currently, I don't have a particular problem. I was just curious where
to look and how to proceed when encountering such a mix of variables.
Best,
Stefan


On Tue, Jun 2, 2009 at 10:04 PM, Robert A Yaffee <bob.yaffee@nyu.edu> wrote:
> 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
>> > *
>> > *   For searches and help try:
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>> > *   http://www.stata.com/support/statalist/faq
>> > *   http://www.ats.ucla.edu/stat/stata/
>> *
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