🚀 go-pugleaf

In article <4795823@mtsg.ubc.ca> John.B.Collins@MTSG.UBC.CA writes:
>The issue of phi coefficients in factoring dichotomous data is a RED HERRING.
>If the data are dichotomous, SAS, SPSS and other packages will yield a matrix
>of PEARSON correlations, NOT phi coefficients.  True, extreme p values will
>skew the data, but that's because of the DATA, not the correlation matrix.
>You'll know if this is a problem in your particular data set if you get
>Heywood cases (loadings greater than 1.00).  But until this becomes an
>actual problem, go ahead and factor.  The issue of scaled loadings reflecting
>differential "skill levels" calls into question when in the research sequence
>the factor analysis is performed. IRT (Hambleton et al) deal effectively with
>this question.   John

Phi coefficients ARE Pearson correlation coefficients computed on
dichotomous data. The issue is definitely not a red herring, but no one
in this discussion has brought up the major problem, so I'll repeat the
basics of what I've posted here at least twice in the past:

The problem with running SPSS FACTOR or SAS PROC FACTOR on a set of
dichotomous variables is that both of these assume a linear model; that
is, they assume that the regressions of the observed variables on the
underlying factor(s) are linear. This cannot be true for dichotomous
variables. You are therefore misspecifying the model when you do this.
For verification and explanation of this issue, see David Bartholomew's
_Latent Variable Models and Factor Analysis_, or for a simpler exposition,
Roderick McDonald's _Factor Analysis and Related Methods_. As to the
question of how badly this messes things up, that will depend on the
data itself. Sometimes this may provide a reasonable approximation, other
times not. If you don't know ahead of time when it will and when it won't,
I'd be pretty careful about it.

Anyone very interested in this issue might check archives for this list,
as well as the spssx-l list and the edstat-l lists (I don't remember
which one I posted the lengthier discussions to) to see the rather lengthy
post I made a while back explaining some of the results of this problem.

--
 David Nichols        Senior Statistical Support Specialist         SPSS, Inc.
 Phone: (312) 329-3684     Internet:  nichols@spss.com     Fax: (312) 329-3657
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 Any correlation between my views and those of SPSS is strictly due to chance.