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About multivariate response model

Posted: Fri Mar 01, 2019 6:33 pm
by chenr392
Hi everyone

I'm analysing some effect sizes collected from a number of empirical studies, so the data structure is multilevel, with ES nested within studies. ES is my response variable, which comprises of response type A and B. So I'm trying to fit a multivariate response model. I have encountered some difficulties therefore I'm here to seek help.

1) I don't have ES level explanatory variables but only study level explanatory variables. I want to test the influence of these study level variables on A and B. However, for some variables I propose they have similar effects on A and B, and others have differential effects on the A and B. For the variables I proposed to have similar effects, it possible to estimate only one coefficient for each explanatory variable on both A and B, because I'm not interested how different these effects are on A and B. I found a function of "add common coefficient", which will produce an h equation. Can it be used for my purpose? When should the h equation be used?

2) Within each study I have multiple ES reporting both A and B, not only one ES for each type of response. Will this model be useful for such a situation?

3) How to calculate the ICC for this model?

Thank you very much for your help


Re: About multivariate response model

Posted: Tue Mar 05, 2019 9:03 am
by billb
Hi Chenr392,
That all sounds quite complicated. Perhaps a starting point would be to fit separate univariate models for the type A and B responses you could then look at the estimates produced.
I would then be tempted to fit a univariate model but with indicator functions to identify A and B so that you can test for differences of effects on A and B so model something like
y_ij = b0 + b1* B + b2* x1 + b3 * x1*B +... + u_j + e_ij
then b1 identifies differences between types A and B, b2 gives effect of x1 on type A and b3 gives differential effect (and if zero can be removed and then you have common effect). If you expert different variability then you can make random part u_0j + u_1j*B for example

In terms of other questions I think 2 is easier in this univariate formulation as you are not matching each ES for A with ES for B which sounds like it would be difficult here and thus make multivariate hard.

You can work out ICC fairly straightforwardly - in simplest model it is simply sigma^2_u / (sigma^2_u + sigma^2_e). If you decide to make random part depend on A/B then it should still be straightforward.

Hope that helps