[R-sig-ME] MCMCglmm: can one combine different prior distributions in one model?

[Jarrod Hadfield]

Hi,

Having a parameter expanded prior of

V = 1, nu = 3, alpha.mu = 0, alpha.V = 2.5^2

gives a half-scaled-t prior on the standard deviation with df=3 and scale=2.5 (which is the same as the default brms prior you stated).

Depending on the scale of the data I would think this could be a strong prior, so I’m not sure what is the motivation for making it the default?

Cheers,

Jarrod


From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on behalf of claudia.kasper-voelkl--- via R-sig-mixed-models <r-sig-mixed-models using r-project.org>
Date: Monday, 23 January 2023 at 07:34
To: r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
Cc: esther.ewaoluwagbemiga using agroscope.admin.ch <esther.ewaoluwagbemiga using agroscope.admin.ch>
Subject: [R-sig-ME] MCMCglmm: can one combine different prior distributions in one model?
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Dear list,

We are currently investigating heritability of protein efficiency in pigs. Protein efficiency is the amount of protein found in muscle tissue over the amount of protein in the feed an animal ingested over a certain period. By design, this variable is bound between 0 and 1, and it is quite narrowly symmetrically distributed (mean = 0.39, SD = 0.04, min = 0.18, max 0.64).

We ran an analysis with MCMCglmm on data from around 1000 pigs from a paternal half-sib design, an animal model which contained two random effects (an animal effect and litter effect). There were no convergence issues, and the model diagnostics we checked (trace plots, autocorrelation, Heidelberger diagnostic, and effective size) looked all very reasonable. The heritability was 0.43 [0.29, 0.58] and the litter effect 0.12 [0.07, 0.17] - 95% credible intervals in brackets.

modelH <- MCMCglmm(prot_eff_carcass ~ year + slaughterweight + treatment2 + sex + age + temp + treatment2*age + Y_change1*age + slaughterweight*sex + treatment2*sex,
                   random = ~animal+sibship, family = "gaussian",
                   prior = prior, pedigree = ped, data = herit2, nitt = 2000000,
                   burnin = 100000, thin = 1000, verbose=FALSE)

Following a reviewer's request, we reran the same model (and others, with other traits that have a wider distribution) in ASReml-R, and we got quite some differences for protein efficiency in the results from ASReml-R and MCMCglmm [ASReml-R heritability: 0.60 � 0.08; ASREMLR litter effect: 0.00006 � 0.000003]. MCMCglmm estimated lower heritability and higher litter effect. The models for the other traits, however, yielded pretty much the same estimates.

In order to verify results from both packages, we simulated data similar with the same heritability from MCMCglmm (0.43) and mean as estimated in the real dataset, but with a range of different litter effects. We observed that ASReml-R estimated the true litter effect more accurately, whereas MCMCglmm overestimated the litter effect and underestimated heritability throughout. We ran the same model in brms (with the default prior [student_t(3, 0, 2.5)]) and we had similar results as with ASReml-R.

We further played around with the priors (all weakly informative priors), combining the standard prior [inverse gamma with V=1 and nu=0.002] for the additive genetic variance, the standard prior [inverse gamma with V=1 and nu=0.002] for the residual variance and a parameter-expanded (for the litter effect) (with V=1, nu=1, alpha.mu=0, alpha.v=1000). Surprisingly, the 'combined' prior gave the similar results as ASReml and brms for simulated and real data. Using the parameter-expanded prior for both additive genetic and litter variance results in dramatically underestimating heritability [real data: 0.04; for simulated data: 0.00003]. Is it even permissible to combine the two in one model? Since brms is taking a much longer time to run for the same model, and we are quite familiar with MCMCglmm already, we would prefer to stick with it.

prior4 <- list(R = list(V = 1, nu = 0.002), G = list(G1 = list(V = 1, nu = 0.002), G1 = list(V = 1, nu = 1, alpha.mu = 0, alpha.V = 1000)))

We will appreciate any comments over this issue.

Best regards,

Esther Ewaoluwagbemiga and Claudia Kasper

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