Commonly, I use the MANOVA statement in the GLM procedure of SAS (general linear models) to perform a multivariate analysis of variance on continuous dependent variables. Also, I use the statement DIST=BIN in the GENMOD procedure of SAS (generalized linear models) to perform logistic regression on binomial dependent variables.
To my knowledge, I cannot perform a MANOVA using binomial dependent variables, but I suppose that some way to do it must exist.
In fact I would like to use a multivariate logistic regression. Show can I perform it in SAS?
I think neither GENMOD nor LOGISTIC can treat multivariate analyses
The paper that you attached deals with a multiple (several independent variables), but not a multivariate logistic regression (several dependent variables).
Dear Giovanni
You could do an analysis equivalent to a Manova by doing several univariate analysis with the wished alpha adjusted by the number of response variables with a procedure of multiple comparision like Sidak (http://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction) or Bonferroni's http://en.wikipedia.org/wiki/Bonferroni_correction.
Dear Guillermo,
your proposal seems interesting. May you explain me better the method in practice? How can I do it in SAS?
In the case of bonferroni it is very easy. Assume that you have 5 response variables and that you are comparing k treatments, then you could use the logistic regression model but instead of considering if the p value is less than alpha, you have to consider if your p value is less than alpha/5 (the number of response variables). If this happens for any of your response variables, you have different effects for any of the treatments, if not, you could not reject the null hypotesis.
Sidak is the same but your alpha of comparision is obtained solving the equation for alpha1 (http://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction)
Many thanks Guillermo.
May you provide any reference for this method in order to cite it in scientific paper?
Dear Giovanni
If the m response variables may be considered locally independent and that polychoric correlation between them is unidimensional, this problem could be analysed with IRT (Item response theory). This is usual when you have test in education or psicological applications.
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