# Factor analysis and regression

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)

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?

• As far as I know, factor loadings (and hence scores) are only defined up to a multiplicative constant, so the signs are not meaningful Jun 5 '12 at 13:48
• It sounds like you are using the same variables as explanatory variables for your regression as you used in the factor analysis? If so, the approach is probably not very helpful - see stats.stackexchange.com/questions/32319/…. If not, then what variables are you using for explanatory variables? Aug 4 '12 at 20:35
• You can take a look here: (pdf) for a discussion on using factors scores in regression (see in particular Table 1, 3rd column, for the case of independent variable observed, dependent variable factor scores) Jun 30 '18 at 20:35