I have two groups of continuous* variables - let's call them MF (5 variables) and OR (2 variables), plus some demographics. It has been previously found that the MF are associated with one of the OR variables, and I'm now trying to find out how useful is it to add the other OR variable. I think this means that I am trying to find out what is the increase of the explained variance when I add OR2 to a model which already has OR1. Because I have multiple predictor and outcome variables**, I use multivariate multiple regression, like the one I found here: Multivariate multiple regression in R. Now, I can do the regression in R with lm() and with GLM in SPSS, and I can get the Pillai's trace for the predictors (about .30 for OR1 and .15 for OR2 in the model where both are in) and the parameter estimates, R-squareds and t's for individual predictors by each parameter - but what I don't know is how to compare the two models (the one with only OR1 and the one with both OR's) so I would get one value/test as an estimation of the difference between them. So how can I compare the models?
edit: I simplified the question according to what I learned.
edit: AIC or BIC in R don't take multiple responses, so that didn't work. Can I simply add the error sums of squares of all the predictors together and divide that by the sum of all total sums of squares (of individual predictors) to get a r-squared (or AIC by correcting for number of parameters) for the whole model, and then compare these between the two models?
edit: I tried anova(model1,model2) in R, but it gives suspiciously the exact same Pillai's trace as the model2's second parameter (OR2) has. I assume this kind of coincidence is not a coincidence, but a sign that anova cannot handle multivariate models like that.
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*) Ordinal variables really, as they are questionnaire data. OR are two single-items with a range from 1 to 11, so the variables are discrete with 11 different values. MF are 5 factors from a questionnaire with a response range from 0 to 5, but because they are means from several items, the values are more than just the 6 discrete values and so I treat them as continuous (not sure if this is appropriate though).
**) As questionnaire data, there is no experimental manipulation, so I designate of one group as predictor and the other as outcome arbitrarily. Theoretically, it would make more sense that the MF predicted the OR, but when my question is about the explained variance, and I assume it makes no difference mathematically which is which, I pick OR as the predictor because I assumed that the comparison of models would be simpler that way.
