I have a question about how to interpret a regression analysis I did following a factor analysis.
I did principal axis factoring (direct oblimin)
I got a 3 factor solution. The three factors were (1) feelings (2) kinship and (3) interactions. (I'm looking at father-child relationships)
Regarding factor loadings, (1) feelings had all positive factor loadings, (2) kinship had all negative factor loadings and (3) interactions had all negative loadings.
I did a multiple regression analysis using the factor scores – saved as regression scores – as outcome variables. I'm not bringing them together to form a total scale, so I don't think I need to do a MANOVA instead, or adjust the p-value.
For (1) feelings, all of my predictor variables have positive beta weights
For (2) kinship, one of my predictors (participation in healthcare) has a negative beta weight
For (3) interactions, again, one of my predictors (participation in healthcare) has a negative beta weight
I'm confused about whether the predictors with negative beta weights actually imply that less participation in healthcare means a higher score on kinship and on interactions. Or whether, because those two outcome variables have all negative factor loadings, should the negative beta be interpreted as a positive beta? (i.e. do the negatives cancel each other out?).
If the latter is the case, do the predictors with a positive beta for outcome variables (2) and (3) actually have negative betas?
Best Answer
Apparently your rotation produced meaningless results, as sometimes happens in exploratory factor analysis. If you want to have straightforward interpretation of your factors, then you would want to either flip the sign manually, or somehow make it work in your software that the signs of the loadings are positive. Your interpretation is kinda correct, in the sense that an increase in healthcare participation decreases the kinship factor score, which, however, in turn means that the variables contributing to kinship factor increase.
Note that you will likely be better off with a latent variable MIMIC model in which you have predictors, a latent variable, and its indicators; in any latent variable modeling software, you can specify one of the loadings to be 1 (the scaling indicator), and then other loadings will follow suit if the indicators are positively correlated with one another. Modeling the measurement part and the causal part jointly will produce more efficient estimates; you will fall into the confirmatory-after-exploratory-factor-analysis fallacy though.