[R-sig-ME] Analysis of unbalanced nested half-sib/full-sib, design with MCMCglmm/lmer

[Gustaf Granath]

In a simple univariate case the animal + dam model may give the same 
output as a sire + dam model. However, for multivaraite analyses (if you 
intend to run such analyses as well) with messy data (variances close to 
zero, unbalanced, low sample size, noisy), I have experienced that the 
sire + dam model gives much more reliable estimates (less auto 
correlation etc) and is probably a better option if you have a classic 
half-sib design.

Gustaf Granath

> On Tue, 6 Aug 2013, David Boukal wrote:
>
>> Question 1: How do the quantities from Lynch & Walsh relate to the VCV
>> components provided by MCMCglmm or lmer?
> Same. Note your h2.m2b and h2.m2c as written are inconsistent with this.
>
>> Question 2a: Can the animal model of Wilson et al (2010, WAMWiki) be
>> applied "as-is" with the appropriate pedigree to this nested design and
>> what are the pros/cons of (not) doing that?
> Yes. No cons.
>
>> Question 2b: Why do the results for heritability differ when I use both
>> father and mother as explanatory variables as opposed to using only
>> mother and supplying the pedigree (= essentially the
>> animal+mother+father columns of my data including the NA rows for parents)?
> If no animal term, ped is not used, I would think. So, m2b == m2c.
>
>> Question 3: MCMCglmm course notes suggest DIC may not be meaningful to
>> use when priors differ. How does one select between models that differ
>> in the number of random effects then?
> If you are interested in maternal effects, you should look at the
> confidence interval for mother in your m2.
>
>> So model m1 has the lowest DIC, but the heritability estimate is kind of
>> high...
> Eyeball the fullsib and halfsib intraclass correlations.
>
> More generally, for the half-sib design, the A+D (or A+maternal) model is
> equivalent to your sire+dam model, so that m2b and m2 should fit the data
> equally well in terms of likelihood (in a frequentist LMM). In that case,
> the DIC differences reflect how model complexity is being assessed.  I
> believe there are a few different ways one can calculate DIC for RE
> models.
>
> For one simulated dataset
>
> Paternal half-sib design
>
> 100 sires, nested 10 dams per sire, 5 offspring per mating,
> true h2=0.5
>
> Relation r      JSE
> Halfsib  0.1478 0.0092
> Fullsib  0.3254 0.0169
>
> Program  -2*LL or Dev A        Maternal  Sire    Dam     E        DIC
> Wombat    3136.830    0.89100  -         -       -       0.56981  -
> Wombat    3136.618    0.83105  0.025198  -       -       0.59548  -
> Wombat    3136.618    -        -         0.20777 0.23295 1.01101  -
> MCMCglmm  5652.37     0.9163   -         -       -       0.5547   6987.498
> MCMCglmm  5733.77     0.8858   0.00596   -       -       0.5731   7035.543
> MCMCglmm  7195.74     -        -         0.2147  0.2311  1.015    7590.391
>
> MCMCglmm, default options.
>
>
>
> Cheers, David Duffy.