Suppose you have some covariates X1, X2, X3, X4, X5 and you want to create a regression model where there are two response variables : Y1 and Y2.
In the past, I have approached this problem by creating two separate regression models:
Y1 ~ f(X1, X2, X3, X4, X5)
Y2 ~ f(X1, X2, X3, X4, X5)
However, now I am interested in learning about statistical models that can jointly model this data together, for example:
P(Y1, Y2) ~ f(X1, X2, X3, X4, X5)
I think that this approach would allow for modelling potential correlation structures with Y1 and Y2.
My Question: Do such models exist that can jointly model multiple responses - is this a popular topic in statistics? Are there any standard references and software implementations (e.g. R programming language) for these kinds of models? The only thing I could find was the following : https://www.jstatsoft.org/article/view/v084i04.