Re: Covariance structure for random effect

ggorjan wrote:
Hello!

I am analysing data on behaviour of animals. I have a factor at 1-level
i.e. fixed effect and I also added animal indicator as 2-level i.e.
random effect of my model, as there is considerable variation between
animals. Very often one assumes that 2-level units are independent, but
in my case this might not be the case, since animals within one level
of a factor were in contact and might influence on each other.

I could model this dependency as say multivariate normal with
particular covariance matrix for 2-level within each factor, but I have
not came accros any such examples. I a bit skeptic in amount of
information to estimate "many" covariance components. For now compound
symmetry, unstructured and Toeplitz (in SAS parlance[1]) structures for
covariance matrix have come to my mind fot this task.

Does anyone have any experience in this type of models? Any
suggestions, comments, pointer to relevant literature are more than
welcome.

Thanks!

[1]http://v8doc.sas.com/sashtml/stat/chap41/sect20.htm#mixedspcovstruct

You're not getting much response. :-)

I haven't done anything like this, but it I guess you would like to include the other animals in the group as a covariate, but the covariate is actually the response variable. To me, this looks conceptually similar to spatial models (e.g. CAR models), which might help. There's a nice book by Banarjee, Carlin and Someone Else on hierarchical spatial models: it uses R and BUGS, which will help.

If you have a situation where you have dominance hierarchies, then you might be able to do something cunning with ranks in BUGS, but I haven't thought that through (and it would depend on the type of data: identifiability and all that).

Alternatively you could try asking at the Quan_Gen group:
<http://groups.yahoo.com/group/Quan_Gen/>
someone there must have come across the same problems.

Bob

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Bob O'Hara
Department of Mathematics and Statistics
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