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I am aiming to create an index and I have 4 individual variables that I want to put in one component. I would use this index as an explanatory variable in multiple regression analysis later on.

  1. However, as the correlation between those 4 individual variables is low and they are mostly categorical and binary (but I have normalized them), it doesn't make sense to do a principal component analysis. Is this correct?
  2. As an alternative I thought I could do a confirmatory factor analysis and then create factor scores. Can I use those factor scores then in the regression as explanatory variable or do I introduce then any kind of bias?
Laura
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  • What do you mean by correlations of your "categorical" variables (those which aren't binary)? – ttnphns Jul 01 '21 at 12:05
  • With low correlations it is unwise to do factor analysis. All the more confirmatory one, as you don't have a factor structure to test. It is probably better to leave your 4 variables as they are, to use them as individual predictors in your regression. – ttnphns Jul 01 '21 at 12:10
  • Sometimes people still create an index out of uncorrelated items, such hodge-podge construct is called a battery. See https://stats.stackexchange.com/a/260682/3277 – ttnphns Jul 01 '21 at 12:13
  • Yes- categorical as in there are e.g. 4 categories to choose from (non-binary). In case of running a CFA with low correlation, does that show in factor loadings being low <0.4? When running a CFA with my 4 variables, the fit indicators are all better then the cut-off. This still does not support using the CFA to create an index? – Laura Jul 01 '21 at 13:15

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