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Can hb utilities (zero-centered diffs) be used for factor analysis?

Good day!
Our team plans to use factor analysis to verify if the attributes used in our Conjoint study were indeed independent, or if there are overlaps. In working with this, I used the zero-centered diffs HB utilities for the attribute levels generated in the conjoint model as data input. I’ve encountered in the output however, that the correlation matrix is not positive definite, hence the results may not be sound.

I’d like to verify if zero-centered HB utilities in a conjoint study is appropriate for use in running factor analysis, or other methods may be better for this purpose?

asked Feb 7, 2013 by anonymous

1 Answer

0 votes
Good morning,
1) Using zero-centered diffs doesn't have to generate not positive definite matrix. Most of the time correlation matrices for z-cd and raw utilities are quite similar and you can use them for principal components or factor analysis. With very similar results.
2) You should check why your matrix is negative definite. Most often it comes from extreme collinearity  in your data set. Collinearity can happen for utilities between attributes or within attribute. Although some level of collinearity (and dependence) between attributes is common in conjoint utilities it's rarely extreme enough to lead to npd matrix. On the other way you can easily have trouble stemming from within attribute correlations. E.g. all 2 level attributes have perfectly correlated utils no matter if they are raw or rescaled. Perfect correlation between 2 variables always leads to npd matrix.
And here comes simple answer for your trouble - remove one level from each attribute:) then  factor analyse.

But maybe my first question should be, why are you trying to check independence of attributes with utilities? In Cbc's we often want independence of attributes in our design, not in utilities. The simplest test would be some chi square between attributes in exported (spss) data file. You can export from SMRT.

and good luck with you data.
answered Feb 7, 2013 by lkomenda Bronze (2,830 points)
edited Feb 7, 2013 by lkomenda