[R-sig-ME] observation level random effects/kinship model

[Ben Bolker]

Juliet Hannah <juliet.hannah at ...> writes:

> 
> All,
> 
> I was reading the following post:
> 
> https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005184.html
> 
> which discusses why an observation-level random effect does not make
> sense in the linear mixed model
> case.
> 
> Does anyone know of any references that discuss this?
> 
> And for the genetics folks out there, isn't this what the kinship
> model is: an observation-level random effect
> that is correlated by degree of relatedness?

  I don't know of an immediately useful reference (other than, say,
the theory sections of Pinheiro and Bates 2000 or Littell et al or
some other mixed-model book -- and these wouldn't specifically answer
your question, they would just answer it implicitly).  But I would
be happy to hear about one.

  The issue is that in the standard definition of the mixed model
there are random effects (sometimes called "G-side" effects, for
grouping terms) and there is *also always* assumed to be a residual error
term, which is normally distributed independently among
observations in typical cases but can be multivariate normally
distributed (so-called "R-side" effects, "R" for residuals)
in some examples.
   Because mixed models always include a residual term by
convention, including an observation-level random effect would
just amount to partitioning the residual variance into two (unidentifiable)
terms, one corresponding to the residual (R) term and the other
corresponding to the grouping term.
  I'm not a geneticist, but I believe that the kinship model
is inducing a correlation on the *residuals* (an R-side effect)
rather than on a variance associated with a grouping factor.
If you could eliminate the residual error term or equivalently
fix its variance to zero (or very small), you could add a correlated
random effect as a G-side effect (although I think you would have
a hard time finding a mixed model package that allows for correlation
among G-side effects -- you'd probably have to code your own model
via ADMB or WinBUGS ...) -- but at least the standard R packages
(nlme, lme4, glmmADMB) don't let you do that.

  In GLMMs for families that do *not* have an adjustable scale parameter
(e.g. the most typical examples -- Poisson, binomial), there is
no normal residual error term included in the model, so it's OK to 
include an observation-level random effect.