# Using factors scores in a multiple regression [duplicate]

Can factor scores be used as dependent variables in regression?

Also, I want to see if demos (e.g. age, SES etc) predict performance in five different cognitive ability tasks. For each task I have the accuracy and speed of response. Would it be worthwhile attempting to run a factor analysis on these ten variables. So I could use these factor scores as my dependent variable and the personality variables as my predictors in multiple regressions.

Or would it be more logical to run a multiple regression for each composite score (one for every cognitive task)?

Any help would be appreciated!

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## marked as duplicate by StasK, gung, whuber♦Mar 12 '13 at 3:14

When you have multiple dependent variables, there is always a question of how you should analyze the situation. The basic question is how you understand these variables to be related to each other. If you believe they are unrelated, then you can safely run several multiple regression analyses using each DV in turn. If they aren't unrelated, then the relationships amongst them need to be taken into account somehow. If they are multiple measures of the same underlying construct, then they can be combined into a single variable and used as a single DV. For example, consider a personality questionnaire that attempts to measure extroversion. There will be a number of questions that are all understood as measuring the same thing, viz., extroversion. In this case, the responses to the various items are combined (typically by adding them up or averaging them), and you can then run a single multiple regression model with the combined score as a single DV.

The question is, whether your measures are like that. How should you determine this? First, your theory, or the main theories operative in your field, may provide an answer. If they don't, or you want to check them, you can run some analyses on your data. A factor analysis is one such possibility; if your measures load onto a single factor, you're good to go. If they load onto more than one factor, you should perform a non-orthogonal rotation such as oblimin, and check the correlations amongst the factors; if they are low enough for your satisfaction, then you can treat them as unrelated as discussed above. Another possibility is to run multiple regressions with each DV in turn and save the residuals. Then you can see if the residuals are correlated with each other; if they're not, you're fine.

If your measures are related to each other, you need to account for that somehow in your modeling. Presumably the best approach would be a structural equation model that allows you to specify the manner in which the measures are related.

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Thanks, @Lolly. I'm not sure you need to switch the accepted answer, though. You can also indicate than answers have been helpful for you by upvoting them (ie, clicking on the right-side-up normal distribution to their left). – gung Mar 10 '13 at 18:42

I see no reason why factor scores cannot be used this way.

As to whether you should run a factor analysis on the 10 tasks, I think it depends on what you are trying to do. If the 10 tasks are well-established and you think they are a good representation of cognitive ability, go for 10 separate analyses.

If you want to try to find some different representation of cognitive ability, then FA may help.

As you probably know, "cognitive ability" is a topic on which there is little agreement. Is it one thing? Several things? A great many? Is there a "g" factor that corresponds to "overall ability"? Do you take a Gardnerian view that there are multiple intelligences that are only modestly (if at all) related? Or a Sternbergian view that there are several abilities that are somewhat related? Or some other view?

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Thanks that's a great help. But within any one multiple regression can i use a factor score as the dependent variable and another set of factor scores as predictors? – Lolly Mar 10 '13 at 16:45
I don't see a reason why not, as long as the various factors are based on different variables. – Peter Flom Mar 10 '13 at 18:02