[R-sig-ME] overlapping multiple membership specification in lme4

[i white]

Heidi,

I know nothing about multiple membership models but your problem reminds 
me of what plant breeders call a diallel cross design, in which (e.g. 
22) different lines of plants are crossed and the progeny measured. If 
we allow different line effects for male and female parents, this is a 
conventional two-way anova, but if we assume that the line effect is the 
same whether parent is male or female, we have something like your 
situation, in that the model is

y(ij) = const + (alpha)i + (alpha)j + ...

instead of

        const + (alpha)i + (beta)j + ...

for the cross of male parent from line i and female parent from line j. 
Analysis requires a special model matrix which is the sum (overlay) of 
the model matrices for male and female parents, with rows corresponding 
to between-line crosses consisting of two 1s and (in this case) 20 zeros.

Heidi Colleran wrote:
> Dear List,
> 
> I'm a PhD student writing to ask for some help on specifying a model in R.
> I'm currently using the lme4 package.
> 
> I'm trying to analyse how migration effects womens fertility rates in a
> sample of 22 groups (villages). I have a sample of ~1500 women who were
> born and continue to live in one of the 22 groups. I treat the model as
> women clustered within groups. Each woman has an origin group ID and a
> current group ID, so for women who never migrated these ID numbers will be
> the same. I want to obtain variance parameters for the different groupings,
> to see whether origin or current group has a greater effect on fertility
> rates, with a view to then seeing if other group-level predictors explain
> some of the variance, but I'm not sure if I have specified the model
> correctly, or if I need to make some changes to the data (for example
> weighting the memberships somehow).
> 
> I started with (what I think is) a cross-classified model of the form
> (y~1+(1|originGroupID)+(1|currentGroupID)),
> but given that the groups themselves are exactly the same thing, and that
> membership in them overlaps, I am worried that this will cause problems for
> estimating the group variances and covariances, or that this specification
> perhaps doesn't make sense. Should the groups be coded differently?
> 
> If anyone could point me in the direction of some references specific to
> this kind of overlapping structure, or indeed offer some advice as to
> different ways I could specify the model, or recode the data somehow, I
> would be extremely grateful.
> 
> Many thanks,
> 
> Heidi
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