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

[Dacvid Duffy]

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.

| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v