I just browsed through this wonderful book: Applied multivariate statistical analysis by Johnson and Wichern. The irony is, I am still not able to understand the motivation for using multivariate (regression) models instead of separate univariate (regression) models. I went through stats.statexchange posts 1 and 2 that explain (a) difference between multiple and multivariate regression and (b) interpretation of multivariate regression results, but I am not able to tweak out the use of multivariate statistical models from all the information I get online about them.
My questions are:
- Why do we need multivariate regression? What is the advantage of considering outcomes simultaneously rather than individually, in order to draw inferences.
- When to use multivariate models and when to use multiple univariate models (for multiple outcomes).
- Take an example given in the UCLA site with three outcomes: locus of control, self-concept, and motivation. With respect to 1. and 2., can we compare the analysis when we do three univariate multiple regression versus one multivariate multiple regression? How to justify one over another?
- I haven't come across many scholarly papers that utilize multivariate statistical models. Is this because of the multivariate normality assumption, the complexity of model fitting/interpretation or any other specific reason?