I have a statistical quandary I'm trying to solve, hopefully someone here can help.
I have a data set with several dependent variables measured as ordinal Likert items and I want to measure the impact of a single independent variable on these. Since it's multiple dependent variables and several independent variables (one important one and several as controls), I'm considering multivariate multiple regression.
I've never actually used multivariate multiple regression before, but I realize that it technically (like m/anova) requires continuous dependent variables, however in my field it's not an uncommon practice to treat Likert items as continuous, that is using Likert-items (though preferably full Likert scales) with parametric tests, such as ANOVA.
I'm not interested in the parameter estimates (though the marginal means might be interesting), but rather in comparing how much of the variance in each of my dependent variables can be explained by a specific independent variable (partial eta squared). Is this reasonable? Outside the obvious problem with Likert-items and parametric tests? (I tested univariate ANOVA both parametric and non-parametric, Kruskal-Wallis H, with significant results).
Alternatively I could do individual ordinal logistic regressions for each dependent variable, but then the comparison becomes problematic (comparing pseudo r-square across for different models with different dependent variables), or I could make an index variable out of the dependent variables (they are measuring the same overall theoretical construct) and do a linear regression with the index as dependent, but that means I can't compare the effect of my independent variable on the individual dependent variables.
Finally, I considered doing the multivariate multiple regression, while also doing individual simple ordinal logistic regressions for each dependent variable with just the important independent, just to give an indication of whether the multivariate regression is reasonable based on the pseudo r-squares, and support the results if so.
