# [R-sig-ME] MCMCglmm: ixn between binary family-level factor and us() random effect

Sat Feb 5 11:49:18 CET 2011

```Hi Paul,

random =
~us(at.level(asthm,1):offpar.f):famid+us(at.level(asthm,2):offpar.f):famid

Does what you want, but I would think hard about what the terms in
us(offpar.f):famid mean. For example the diagonals of the 3x3
covariance matrix are the mother, father and offspring variances, but
only the last variance can be uniquely estimated with all residual
structures (because there are multiple offspring but only a single
mother and a singe father within a family). For example, these
varances would could not be uniquely estimated if gender specific
residual variances were fitted,  and would be partially confounded in
your case where you estimate a common variance across offspring and
both parents.

The off-diagonals (assortative mating, mother-offspring,
father-offspring covariances) can be uniquely estimated but it would
make much more sense to do this at the residual or phenotypic level.
You could probably do it using SIR models but I have not documented or
tested them yet. You could try some of the SEM models used by people
studying human genetics. I believe Mx is widely used, and if you can
get hold of an accompanying book "Methodology for Genetic Studies of
Twins and Families" (1996) by Neale, it is excellent.

Cheers,

Jarrod

The off-diagonals which represent assortative mating

Quoting Paul Johnson <Paul.Johnson at glasgow.ac.uk>:

> I'm fitting models to estimate mother-father and parent-offspring
> covariances, using
>
>    random = ~us(offpar.f):famid
>
> where offpar.f is a factor with 3 levels: offspring, mother, father
> and "famid" is the family ID. This allows me to compare the
> strengths of mother-offspring and father-offspring correlations
> within familes. The next step is to compare these covariances
> between asthma families (AF) and non-asthma families (NAF). I.e. I
> want to estimate three covariances within each level of the NAF/AF
> factor while setting the covariances between NAF and AF families to
> zero. The structure of the 6x6 covariance matrix should be
>
>    VAF   0
>    0     VNAF
>
> where VAF and VNAF are 3x3 US covariance matrices and the 0s are 3x3
> blocks of zeros.
> How can I specify this in a formula? I've tried various random
> formulae based on what I found in the MCMCglmm course notes and this
> list but with no success.
>
> Thanks for any help,
> Paul
>
>
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