# Multivariate regression

I am just wondering about the appropriateness of multivariate regression in my research design. As an example, say I have three different dependent measures of similar constructs (e.g. "academic achievement", such as school marks, GPA scores, SAT scores) and accuracy responses on four different trials types (e.g. accuracy on red, black, blue, and white trials) - in two different schools.

If I'm interested in how the three measures of academic achievement predict accuracy on the four trial types (red,black,blue,white), should I be running one multivariate regression (with the two schools as an interaction variable) or three different regression (with the two schools as an interaction variable, with school marks, GPA, SAT scores in separate models)? I am not really interested in holding the other academic achievement measures constant, as they are all likely similar measures of a similar construct? By holding them all constant, I am worried that I will be wiping out any effects that did exist as they are all measures of similar things.

Any answers with minimal maths/equations would be much appreciated. Thanks!

## 1 Answer

I would setup a multivariable regression (not multivariate in predicting all trial outcomes at once like in Manova).
I would construct a model like this:
lrm(trial_colour~GPA_Scores+SAT_Scores+school_marks)

interaction terms do not come from the schools, instead interaction terms are from this form e.g. GPA_Scores*SAT_Scores if these two measures would have an interaction with each other (e.g. BMI and Weight)

I would do this for eacht trial_colour (that's a metric variable, right). Don't forget to plot confidence intervals, you can even do plot all 4 trials in picture (including CI's)

• This answer seems not to address the intent of the question: given there are four responses, what would be the advantages and disadvantages of modeling them as a multivariate response rather than as four separate responses (as you recommend here)? – whuber Oct 9 '18 at 19:05
• I interpreted this as mutlivariable Regression related question, a common misconception among people with "with minimal maths/equations" Essentially there is no Problem with doing a multivariate regression, but this often used to measure a System, instead of Independent assessments. – Nuke Oct 10 '18 at 14:29