Linear regression or multivariate regression?

#1
Hi there,

I am pretty much a newbie in statistics and I hope you can help. I have an experimental design where I analyze three time-windows before the stimulus onset and three windows after. I have three conditions under which the brain responses are obtained. I want to see to what extent does the pre1 predict the post1 (the same for pre2 -> post2 and pre3 -> post3) in different conditions and whether the regression coefficients between the conditions differ significantly.
What is better, to run a linear regression for two conditions at a time (1 vs 2, 2vs 3, 1 vs 3) and then comparing the coefficients by creating a dummy variable and creating an interaction between it and the predictor
or to run a multivariate regression (e.g. DV = post1, post2 and predictors are pre1 and pre2) in order to correct the possible correlations between the predictors (as I understand it, pre1 can correlate with pre2 because all the data is obtained from the same participants and the brain response in pre1 correlate with the brain response in pre2 in one person)? However, I still didn't find whether it's possible to compare regression coefficients in a multivariate regression.
I am a little bit confused and hope I've explained it understandable enough.
 

noetsi

No cake for spunky
#2
Multivariate regression commonly is linear regression, the linear regression refers to how you estimate the results not how many predictors you have. I don't understand how you would compare the three coefficients by using an interaction term. I am not sure if you have one or three separate dependent variables. While there are ways to approach this (MANOVA for example) I have not seen the approach you suggest used for multiple dependent variables. If you do have one dependent variable than I would think running a multivariate approach makes more sense.

In general you can certainly compare the results on multiple predictors on a single DV.
 

CB

Super Moderator
#3
Multivariate regression commonly is linear regression
People do commonly refer to multiple linear regression as "multivariate regression", but it sounds like this is one of the cases where being finicky about the definition might be worthwhile (victor would be thrilled!) Multivariate regression, strictly speaking, is not the same thing as multiple regression: multivariate regression involves multiple dependent variables. And that is, I think, I what the op is talking about.

I'm not sure that it's the best option here though - I haven't got a good grasp of what the study is about. OP could you expand your description of your experiment and what specifically you are trying to find out, substantively?