Re: Multivariate regression

Posted by Andy W on Jul 25, 2013; 7:32pm
URL: http://spssx-discussion.165.s1.nabble.com/Multivariate-regression-tp5721328p5721366.html

Here is how I have been told to go about this, assuming the initial equations are;

y1 = a1 + b1(x1)
y2 = a2 + b2(x2)

Stack each sample so you have all the y's and x's in the same column, and you have a dummy variable representing the two samples and estimate the model;

y = a + b3(x) + b4(Dummy) + b5(Dummy*x)

Lets say here the dummy variable represents the 2nd sample. For the first sample, the last two terms drop out, so you are back to the original equation;

y = a + b3(x)

For the second sample, because [Dummy*x] equals [x], you end up with;

y = (a + b4(Dummy)) + (b3+b5)*(x)

Which you can do the math and see how it reduces to the second group equation estimated separately. So in the combined model the interaction term tests the differences between slopes. Note by construction the intercepts are accounted for, so changes in location between samples is "controlled". This extends to multiple variables and different GLMs.

In concordance with Bruce's advice, if stacking and estimating the models doesn't make any sense (e.g. the error variances or distributions are non-sensical to fit using the same model), then you will not want to do this. I have no idea how this compares to Gene's advice about SEM restrictions.