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Hi,

I am running a multivariate MLM with multiple responses. It is basically a three level model assessing change in time of certain responses. If I add the some coefficients as common coefficients for my responses (the ones that I want to control for all my responses such as common participant characteristics), do the parameters pertaining to the common coefficients refer to the estimates for the whole model taking into account all the responses? I am having a hard time understanding how the common coefficients are estimated. I also have separate parameters (eg time) in the model to understand their effect individually on the responses.

I would greatly appreciate some references pertaining to this issue. The section in the mlwin manual on multivariate models is very short.

Thanks so much

Hi Katekeri,

I think this might be a slight misunderstanding. Essentially if I consider a 2 response case - say I am looking for predictors for weight and height and to make life simple then I have age as a predictor then the correct thing would be to have both the intercept and age as separate coefficients
i.e. weight = a + b age and height = c + d age
If you put age to have common coefficients then you would have
weight = a + b age and height = c + b age
i.e. both weight and height go up by the same amount b for an increase of 1 in age. This makes no sense as weight and height are on different scales!

In general common coefficients are not often used but you might have 2 tests as responses say Maths1 and Maths2 both marked out of 100 and you might be looking at free school meal eligibility (FSM) then having separate coefficients would give
i.e. Maths1 = a + b fsm and Maths2 = c + d fsm
so here you have 2 coefficients b and d that represent the (probably negative) difference in scores in the 2 tests for fsm recipients. Now you might assume that the disadvantage is the same in both tests as they are on the same scale so but fsm as a common coefficent
Maths1 = a + b fsm and Maths2 = c + b fsm
where now b is the common disadvantage across the 2 tests.
So common here refers to the same across responses

Hope that clarifys,
Best wishes,
Bill.

Hi Bill,

This is so helpful. Thank you very much! Yes, I had two subscales of the same test but it is probably more meaningful to add separate coefficients.

Thank you!