🚀 go-pugleaf

Here are responses for my posting regarding the methods
to determine dimensionality of binary items.  Thanks.

Haggai Kupermintz
School of Education
Stanford University

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A method that I find works very well with some data is to factor
anlalyze the matrix of tetrachoric correlations--this is easily done
with the PRELIS program of Joreskog and Sorbom.  Some other methods to
know about are the dichotomous variable factor analytic methods
discussed by Bock (extensions of item response theory for a
multidimensional latent trait space) and Muthen.

Here are some references:

Bock, R. D., and Aitkin, M. (1981).  "Marginal Maximum Likelihood
Estimation of Item Parameters:  Application of an EM Algorithm,"
Psychometrika, 46, 443-459.

Bock, R. D., Gibbons, R., and Muraki, E. (1988), "Full-Information Item
Factor Analysis," Applied Psychological Measurement, 12, 261-280.

Joreskog, K. G., and Sorbom, D. (1988), PRELIS User's Manual, Chicago:
Scientific Software, Inc.

Mislevy, R. J. (1986) Recent developments in factor analysis of
categorical variables.  Journal of Educational Statistics, 11, 3-31.

Muthen B., "Contributions to Factor Analysis of Dichotomized Variables,"
Psychometrika, Vol. 43, pp. 551-560, 1978.

John Uebersax
Bowman Gray School of Medicine
Winston-Salem, NC  27104
uebersax@phs.bgsm.wfu.edu
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This problem has been looked at in the psychometric literature.  The
general recommendation is that you should factor the tetrachoric correlations
rather than product moment (i.e., Pearson) correlations.  Factoring
the product moment correlations will tend to pull for difficulty factors.
That is, items will tend to define factors based on their difficulty,
rather than their content.

Berstein, Ira. (1989). Factoring items and factoring scales are
different: Spurious evidence for multidimensionality due to item
categorization. Psychological Bulletin, 105, 467-477.

Good luck,


David Francis