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My question is simple. I got 4 ordinal variables and I wish to investigate the extent that other 6 ordinal/nominal variables predicts their values. I know that ordinal regression is the appropriate method of predicting those 4 ordinal responses one by one however, since the 4 ordinal variables are also statistically dependent (as chi square verifies) I wonder if there is a method analogous to MANOVA for the continuous case to help me investigate the power of prediction of the 6 IVs to the set of 4 DV taking into account the fact that they are statistically dependent.

Thank you in advance for any help!

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    $\begingroup$ You could do this as a multilevel model or as a structural equation model. $\endgroup$
    – Jeremy Miles
    Sep 15, 2014 at 20:39

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One of possible approaches may be to perform so called optimal scaling on your 4 ordinal response variables. This a procedure to transform ordinal scale into interval scale under the aim to maximize linear correlation among the dependent variables or between the dependent variables and some independent ones. (Some techniques using optimal scaling.)

I suppose you are interested in the latter aim and so you will need Categorical canonical correlation analysis by optimal scaling (OVERALS). Like linear canonical correlation analysis, it maximizes correlation between sets of variables, in your case - the dependent set and the independent set, - but it does it allowing for nonlinear transform of "ordinal" variables into "interval" ones. Aptly may be noticed here that usual (linear) MANOVA is (closely related to) linear canonical correlation analysis, so saying "I want MANOVA" is echoed by "take canonical analysis".

The optimal scaling method just described is an alternative to multilevel generalized linear modelling suggested by @Jeremy in his comment. I can't say which way is "better". The difference between the optimal scaling and the generalizing approaches is that the first assumes a specific mode of explicit transform from ordinal to interval "underlying variable", whereas the second assumes a specific kind of distribution for that interval "underlying variable" by utilizing a corresponding implicit link function and minimizing errors w.r.t. to the observed variable.

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  • $\begingroup$ Thank you both for your comments and instructions. Although I am not quite sure about how I will finally make the analysis, I have a good understanding for the possible alternatives. $\endgroup$
    – Epaminondas
    Sep 16, 2014 at 18:53

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