Covariance structure for random effect

[ggorjan]

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

--
Lep pozdrav / With regards,
Gregor Gorjanc

----------------------------------------------------------------------
University of Ljubljana PhD student
Biotechnical Faculty
Zootechnical Department URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3 mail: gregor.gorjanc <at> bfro.uni-lj.si

SI-1230 Domzale tel: +386 (0)1 72 17 861
Slovenia, Europe fax: +386 (0)1 72 17 888

----------------------------------------------------------------------
"One must learn by doing the thing; for though you think you know it,
you have no certainty until you try." Sophocles ~ 450 B.C.
----------------------------------------------------------------------

[Anon.]

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

--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org

[ggorjan]

Hi Bob!

Nice to hear from you. Please read between the lines.

Yes, CAR is similar. I haven't worked with CAR, but I think that If you
take cities instead of animals and that distance between cities is
equal (I can assume for the start that all animals are "equally
interacting") then my model is conceptually very similar to CAR. Do you
have any experience on amount of information in terms of number of
measurements per unit needed to estimate covariance parameters with CAR
i.e. convergence and mixing issues?

> 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).

Unfortunatelly, I do not have any information on hierarchy, although
this is quite important aspect in behaviour. Btw. the following article
worked on ranks in behaviour.

@Article{Adams:2005,
author = {Adams, E. S.},
title = {Bayesian analysis of linear dominance hierarchies},
journal = {Animal Behaviour},
year = {2005},
volume = {69},
number = {5},
pages = {1191--1201},
URL = {http://dx.doi.org/10.1016/j.anbehav.2004.08.011},
}

>
> 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.

Thanks for this pointer. Are there any other Quantitative Genetic
groups I am not aware of?

Gregor

[Anon.]

ggorjan wrote:
> Hi Bob!
>
> Nice to hear from you. Please read between the lines.
>

I crop up everywhere. :-)

I must admit I haven't tried it, so I couldn't comment: I keep on
telling myself that one day I will, but other stuff gets in the way.

>> 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).
>
> Unfortunatelly, I do not have any information on hierarchy, although
> this is quite important aspect in behaviour. Btw. the following article
> worked on ranks in behaviour.
>
> @Article{Adams:2005,
> author = {Adams, E. S.},
> title = {Bayesian analysis of linear dominance hierarchies},
> journal = {Animal Behaviour},
> year = {2005},
> volume = {69},
> number = {5},
> pages = {1191--1201},
> URL = {http://dx.doi.org/10.1016/j.anbehav.2004.08.011},
> }
>

Thanks: I hadn't seen that. You could re-write the model as a threshold
model, where the outcome is the rank, and then extend it to > 2
categories: it looks a bit like a proportional odds model (check the
Inhalers example in BUGS).

>> 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.
>
> Thanks for this pointer. Are there any other Quantitative Genetic
> groups I am not aware of?
>

Not that I'm aware of.