# Multiple predictors that measure the same concept in regression

I have used three questionnaires in a study that all measure musical training. Each of these three questionnaires (MT1/MT2/MT3) consist of various Likert scales that are averaged to calculate the score of the questionnaire. Now I am interested how musical training is correlated with another variable S (sight-reading ability) in three different conditions. In general my linear mixed model would look like the following, if I had only one variable for musical training:

S ~ cond * MusicalTraining + (1|participant)

The scores of the questionnaires are not surprisingly correlated:

          [,1]      [,2]      [,3]
[1,] 1.0000000 0.3615148 0.7092172
[2,] 0.3615148 1.0000000 0.5723699
[3,] 0.7092172 0.5723699 1.0000000


EDIT

Moreover, when calculating the reliability across all items from the three questionnaires (MT1/MT2/MT3) assessing musical training they show a Cronbach-Alpha of alpha = .86 95%CI [.8, .91].

EDIT END

It seems to me to be too complicated to use all three variables for musical training in the regression and I am also not to sure how to interpret the results of such a model, e.g. S ~ cond * MT1 * MT2 * MT3 + (1|participant).

I tried to run a PCA and use the first principal component in the regression. However, I think a PCA is difficult to interpret if then used in a regression.

Is there any other way to deal with this issue? Could I just average the different measurements of musical training for each each participant and use them as a single variable?

• How is MT measured? Is this one numerical variable? If not, can you describe it? Commented May 22, 2023 at 8:49
• @user2974951 There are three questionnaires that each assess musical training. They all consist of multiple Likert scales that are averaged to obtain the questionnaire score. Commented May 22, 2023 at 9:01
• If you run a reliability analysis in which you enter all items from all the questionnaires simultaneously, what reliability estimate you get? Commented May 22, 2023 at 9:16
• I meant calculating reliability across all items, yes Commented May 22, 2023 at 11:18
• With that alpha & if there are no strong theoretical or other reasons to say these questionnaires would measure different things, I would definitely average all items (from all 3 questionnaires) into a composite measure and use that as the predictor. Commented May 23, 2023 at 12:54