Logistic Regression models with two or more response variables in R/SAS There are a lot of inconsistencies in the literature over what should be the appropriate term(s) for the regression models involving two or more responses, and if they are binary/continuous, for more than one predictor variable.
I have three questions/clarifications regarding these:

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*Multivariate Logistic Regression is one where we have more than one response variable and they are all binary. The predictors could be categorial or continuous.
I also found that this is aka Mixed Effect Logistic Regression by some. Though I still think it is up for debate.


*Multinomial Logistic Regression is one where we have only one response variable which has more than two classes. The predictors could be categorial or continuous.


*Multivariate Linear Regression is when we have more than one response variable and they are all continuous. The predictors could be categorial or continuous.
Can somebody please confirm if these definitions are appropriate and point me in the right direction to execute these regression models in R/SAS/Python with right commands...

I agree with you that the distinction between multiple and multivariate is typically fishy for novices.
However rest assured that, multiple regression is one which considers more than one explanatory variable (aka features). On the other hand, multivariate regression is a model which considers many response variables at a time. As a rule of thumb to distinguish between them

MULTIPLE are the features you include
MULTIVARIATE is the response you deal with

Thus, regarding the models listed

*

*Your description is correct. In addition, Mixed models could be multiple or multivariate or both.


*Your description is correct. Multinomial logistic regression has necessarily a multivariate response, e.g. realizations from a multinomial random vector.


*This is also correct.
To perform multivariate or univariate multiple regression in R use lm. To perform logistic regression you may consider glm.
Multivariate logistic regression is more elaborate because you have to setup a model yoursel depending on the context of study (e.g. longitudinal data analysis, etc.).
For multinomial logistic regression, there is multinom from the nnet package (see here for an example)
