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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?

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  • $\begingroup$ How is MT measured? Is this one numerical variable? If not, can you describe it? $\endgroup$ Commented May 22, 2023 at 8:49
  • $\begingroup$ @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. $\endgroup$
    – Pearson
    Commented May 22, 2023 at 9:01
  • $\begingroup$ If you run a reliability analysis in which you enter all items from all the questionnaires simultaneously, what reliability estimate you get? $\endgroup$
    – Sointu
    Commented May 22, 2023 at 9:16
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    $\begingroup$ I meant calculating reliability across all items, yes $\endgroup$
    – Sointu
    Commented May 22, 2023 at 11:18
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    $\begingroup$ 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. $\endgroup$
    – Sointu
    Commented May 23, 2023 at 12:54

1 Answer 1

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If you can reasonably assume that the three questionnaires measure the same dimension/latent variable representing musical training (MT), you could aggregate the three scores and use a single composite variable representing musical training. Alternatively, you could use the three scores as separate indicators of an MT factor (latent variable) in a structural equation model.

Before doing that though it may be a good idea to run item-level factor analyses with all MT items to see how many factors you would get at the item level (i.e., is there a strong single factor/dimension of MT or multiple factors at the item level?)

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