Multiple outcome logistic regression in R I have a large dataset with multiple binary dependent variables (e.g. y1, y2, y3, y4). yi variables are people's response to their decision making behaviour in different situations. There are many explanatory variables (e.g. x1, x2, ...) which are mainly sociodemographic variables.
I can model each y based on the explanatory variables (e.g. y1~x).
But, all binary dependent variables are correlated and I would like their correlations to be considered in my model. In other words, I would like to model yi ~ xj for all i simultaneously. It can be called a multiple outcome logistic regression model.
I have already tried looking up on the net, glm , and brms packages. None worked for me.
Does anybody know a package that is capable of performing such model?
 A: Maybe nnet::multinom for multinominal logistic regression fits your problem.
If your dichotomous dependent variables are not from a categorical one, perhaps a structural equation model with correlated dichotomous dependent variables is a solution. That would work with lavaan.
A: There are two techniques I would like to suggest. When you have a matrix $Y$ of outcomes and one of predictors $X$, you can use the  Canonical Correlation Analysis, implemented in the CCA package in R. This technique searches for new columns that represent the best linear combinations between $Y$ and $X$. Imagine, you can compute the correlation between two variables and that tells you something about their relationship, but you can't compute the correlation between two sets of columns*! The CCA finds new columns $a_{Y}$ and $b_{X}$ that express the highest correlation between $X$ and $Y$, accounting for the variability within and between the two matrices. Here there is not really a relationship outcomes-predictors, because $X$ and $Y$ are considered at the "same level".
You can also use the Partial Least Square (PLS) analysis, implemented in the pls package. This technique is intimately linked to the CCA, but in this case formally you are looking for the best approximations of $X$ based on their correlation with $Y$.
I won't get in further details for now, but if you need more clarifications please ask.
Here is a tutorial for the CCA. Here another one.
Here is a tutorial for the PLS. Here another one.
*You can compute the correlation of one variable with each of the other ones (pair-wise correlations), but this doesn't take in account the correlation with the other variables!
