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Yes, SAS can perform factor analysis of binary and ordinal data. If you are trying to fit a common factor model, there are two approaches (both known as Latent Trait models):

• The first approach is to run the POLYCHOR macro to create a matrix of tetrachoric correlations (for binary variables) or polychoric correlations (for ordinal variables). You can then do an exploratory analysis (p-values will not be valid) by using PROC CALIS or PROC FACTOR.

• The second approach for binary variables, in the context of item response theory, is the Rasch model. See the Rasch Model item in the list of Frequently Asked-for Statistics.

If you want a principal component analysis of binary data, then use PROC CORRESP or PROC PRINCOMP. Whether to use CORRESP or PRINCOMP depends on whether you are interested in Euclidean or chi-squared distance. You can also use PROC PRINQUAL, but if your data is all binary, PRINQUAL will give the same results as PRINCOMP.

Andrich, D. 1988. Rasch Models for Measurement. Sage University Paper on Quantitative Applications in the Social Sciences, 07-068. Beverly Hills: Sage Publications.

Bartholomew, D. 1987. Latent Variable Models and Factor Analysis. London: Charles Griffin & Company Limited.

van Rijckevorsal, J. L. A., and J. de Leeuw, eds. 1988. Component and Correspondence Analysis. Chichester, UK: John Wiley & Sons.

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