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
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].
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?