Currently, PROC CALIS cannot be used with nominal variables with more than two categories.

If you have binary variables or ordinal variables (regardless of whether you also have continuous variables), and you have the raw data as the input, you can use the METHOD=WLS or METHOD=MLM option in the PROC CALIS statement to fit a structural equation model. Parameter estimates from these models are unbiased asymptotically. These methods also have built-in adjustment for non-normal data so that standard errors can be adequately obtained. However, METHOD=WLS might need a very large sample size. Using other estimation methods for this type of data might or might not yield reasonable parameter estimates, and the standard errors would not be correct. Note that regardless of the estimation method you use, there is always an issue about predicting responses that are outside of the original range.

Alternatively, you can input a covariance matrix that is based on the polychoric and polyserial correlations. PROC CALIS treats this input matrix as the usual covariance matrix for continuous variables and hence the parameter estimates must be interpreted on the latent dimensions (which are continuous) of these discrete variables. This approach can be used with any estimation method and the raw data is not required. However, this approach does not yield theoretically correct standard errors although parameter estimates can still be reasonably interpreted, especially when the sample size is large.

The polychoric correlation is based on the assumption that the two ordinal, categorical variables have an underlying bivariate normal distribution. The polychoric correlation coefficient is the maximum likelihood estimate of the product-moment correlation between the underlying normal variables. To compute the correlation between continuous and ordinal variables, you might use the polyserial correlation. See Correlations in SAS Note 30333, "FASTats: Frequently Asked-For Statistics" which discusses the computation of these correlations.

To create your own matrix of correlations or covariances, see the chapter "Special SAS Data Sets" in the SAS/STAT^® User's Guide.

The following publications have more information about correlations involving non-continuous variables:

• McNemar, Q. (1969), Psychological Statistics, New York: John Wiley & Sons Inc.
• Kotz, S. and Johnson, N.L. (editors), Encyclopedia of Statistical Sciences, Vol 1, New York: John Wiley & Sons Inc.
• Krzanowski, W.J. (2000), Principles of Multivariate Analysis: A User's Perspective, New York: Oxford University Press.

Additional references for PROC CALIS are available in this note.

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