Re: st: model equation multilevel xtmixed

[Leslie Roche <lmroche@ucdavis.edu>]

Hi Hanna,
As a cautionary note, we don't know what your data structure is or
what the individual variables mean, so we can't really comment on
whether this analysis approach is appropriate or not.

That said, using the notation of Rabe-Hesketh and Skrondal, I came up with:

Yijk = β1 + β2χijk +...+ ζ1ij(2) +  ζ2j(3)  + ζ3ij(2)χijk + εijk

where,
ζ1ij(2) is the cow by herd(=farm) interaction (cow nested within herd)
ζ2j(3) is the random intercept for herd (=farm)
ζ3jk(2)χijk is the cow specific random slope term for χ
εijk is random variable representing deviation of observation k on cow
i in herd j.

The notation is a little awkward because of the complexity of the
model (nested random intercepts and a intercept x slope interaction).
The (2) and (3) denote the nested levels, and the ζ1, ζ2, and ζ3
denote the different random effects. I believe Pinheiro and Bates
(2000) do not use the (2) and (3) designations at all.

Hope this helps,
Leslie


On Mon, Jan 24, 2011 at 2:59 AM, Hanna Lomander <Hanna.Lomander@slu.se> wrote:
>
> Dear all,
>
> We are doing a model with random intercept and random slope, as described in Rabe-Hesketh: Multilevel and longitudinal modeling using Stata. The data includes outcomes measured on cows within herds.
>
> The model statement used is:
>
> xi: xtmixed glu i.group dim i.breed i.par i.season || farm: || id:dim, cov(unstructured) reml.
>
> We think that this how the model equation should be written, but since we are not used to this approach we are not sure:
>
> Yijk = β1 + β2χijk +...+  ζ1i + ζ2jχijk + εijk
> where Yijk  = the response of cow i in herd j at occasion k; β1 = the intercept;χijk =  the covariates for cow i in herd j at occasion k; ( We have 3 or 4 more covariates)ζ1j= the random intercept of cow i; ζ2jχijk; = the random slope of cow i in herd j at occasion k; εijk= a random term of cow i in herd j at occasion k.
> What would you think, does this look right to you?  We would be extremely happy for some input!
>
> Best regards,
> Hanna
>
>
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