# Factor scores vs. construct mean scores in regression analysis

I have 48 items in my questionnaire that represent 8 constructs. After conducting an exploratory factor analysis (EFA) with a principal components extraction method and Varimax rotation method, 8 sets of factor scores (FAC_1 to 8) were computed and saved using the regression method.

I've read in academic papers that those factor scores can be used as variables in regression analysis, but the problem is when I do so, the regression test yields no result! (I receive only 0 values!).

Alternatively I computed the mean score of the items representing each construct (resulting in 8 new variables) and used them in the regression test. This method worked, but i'm not sure if it's a correct procedure or not.

### Questions

• Why am I getting zero-values for regression coefficients when I use factor saved scores and meaningful regression coefficients when I use computed mean scores?
• Can the mean scores of each construct instead of its factor scores generated through EFA be used in multiple regression analysis?
• the regression test yields no result! (I receive only 0 values!) This remains mysterious, can you add more details about the problem? Also, do the 8 factors correspond to the 8 constructs (i.e., was it that FA what gave rise to the 8 constructs)? Commented Jul 15, 2012 at 12:37
• Actually first i extracted factors based on Eigenvalues greater than 1, as a result 9 factors were extracted on which none of the items loaded! so i repeated the FA and this time chose "fixed number of factors" and put '8" as the value for the "factors to extract" (because i have 8 constructs in my research model). Then based on the results I deleted 4 items with low factor loadings and then ran the EFA again and this time in "scores" tab i ticked "save as variables" and chose "regression" method. Commented Jul 15, 2012 at 12:57
• Next, i used those 8 saved factor scores (named FAC_1...FAC_8) as variables in regression test. But in the results of the test R, R square, coefficients,... all of them were 0!!! meaning that there's an error! Can u guess what went wrong? Can I use "mean scores" instead of "factor scores" in the regression test? TQ Commented Jul 15, 2012 at 13:01
• Yes, you can use ... instead of ... What is strange though is that the regression failed. Were there any error message? Did you misspecifyed smth? Or is R^2 really very close to 0? I don't know. Commented Jul 15, 2012 at 13:55
• Your guess was right Peter, i used seven of the saved factor scores as IVs and the 8th one as the DV in regression analysis! Now i understand that i shouldn't use the saved factors obtained through PCA in regression analysis. So should I repeat the FA after PCA this time using "Principal Axis Factoring" to save the factor scores to b used in regression analysis? Commented Jul 16, 2012 at 8:37

## 1 Answer

Unlike factor analysis, you cannot just put eight variables into a "regression test" and treat them all equally. One variable has to be the response variable and the others explanatory variables.

Your eight factors have been specifically designed to be orthogonal to eachother. I suspect you have put seven of the factors into a regression as explanatory variables (sometimes called "independent variables") with the eighth as the response variable (sometimes called "dependent variable"). Certainly you would find a low $R^2$ value, and estimates of the coefficient parameters close to zero, in this case.

Using factors as explanatory variables in a regression is sometimes justifiable (although I have some qualms myself - see @whuber's answer here for one reason why it might be questionable). However, the response variable for the regression needs to have been kept out of the original factor analysis. So you can only use your eight factors in a regression if the intent is to explain a ninth variable, one that was not in the original factor analysis.

• Nice response by Peter. Also important is that for your purposes you should be using factor analysis per se, not principal component extraction. stats.stackexchange.com/questions/1576/… Commented Jul 16, 2012 at 5:44