Mike,

I was recently given a 4-option 17-item survey to analyze. The question about multidimensionality came up. I was given the raw file in SPSS and so decided I would start with the more common factor analysis of raw scores, then gradually move into how the Rasch model is more effective. I generated the Winsteps residual matrix and had SPSS run it. I then ran table 23 in Winsteps as a double check and compared the two data sets. What is odd is that for the first 3 of the 4 components, both data sets are virtually identical except that the loading signs seem randomly switched for various items. The 4th component is completely different. I've included the residual matrix I used, the SPSS syntax and the SPSS output. I selected PCA and no rotation, so I'm puzzled. I'm wondering where I went wrong. I've attached the Winsteps control and data file as well. I'd greatly appreciate any help you could provide.

Uve, thank you for sharing your investigation with us.

Factors 1 and 2. The usual convention in Factor Analysis is to report the biggest loading as positive. (The actual sign of the correlation with the hypothetical variable is unknown.) SPSS has coded them negative. Strange!

Factor 3. Agreement.

Factor 4. We may be experiencing rounding error. Suggestion: tell SPSS to extract 6 factors and see if Factor 4 changes.

Thanks Mike. I was more concerned with having done something wrong with one or both analyses. I did try extracting 6 factors per your suggestion, but the 4th factor was still much different in SPSS than Winsteps.

Thanks, Uve. This difference looks like a loss of precision perhaps in the 4-decimal-place correlations.

The Winsteps correlation matrix to 6 decimal places in an Excel file can be downloaded from: http://www.winsteps.com/a/icorfil6.zip