2

I would like to perform factor analysis on a set of responses to a psychological questionnaire. Is there some method that allows me to "weight" each questionnaire item by how important I believe it is (based on the output of some other statistical analyses)? Does it even make sense to ask such a question?

Put otherwise, I would like to impose some sort of Bayesian prior about which questions are more likely to "contain information" or to be "informationally relevant" in a broad sense, or "more likely to be highly loaded on the 'true factors'", etc.

Marcus Emilsson
  • 65
  • 6
  • I'm not aware of. That is a very complex question to be carefully defined. What is being weighted. One potential path of thought is that weighting is embedded into factor rotation (by arbitrary or sophisticated rotation, you can force some variables be loaded more and others less with certain "degree of freedom" for you). Another imaginery path of thought is that during extraction iterations some correlations are being reproduced weightedly by the loadings. Etc. Sorry, your question `in a broad sense` can hardly be answered. – ttnphns May 15 '16 at 11:20
  • Further, using word Bayesian suggests thinking about population parameters and their estimates, but exploratory FA of a sample is very fragmentarily connected with the domain of inferential statistics. Or are you thinking in confirmatory FA? – ttnphns May 15 '16 at 11:24
  • P.S. to just comment1. Please note that some methods of [factor extraction](http://stats.stackexchange.com/q/50745/3277) do a weighting internally (not user-defined): more _communal_ variables (i.e. better fitting into the modelled factor structure) get higher weight during the extraction iterations and so they more strongly define factors. As for factor post-extractional rotations, one may switch off _Kaiser normalization_ during the rotation - to put more weight on the more communal variables. – ttnphns May 15 '16 at 11:55

0 Answers0