[R-sig-ME] MCMCglmm priors and random effects for phylogenetic mixed model

[Jarrod Hadfield]

Hi Alberto,

1/ You can fit it at both levels if you like:

us(1+I2.M1.within.species):phylo + us(1+I2.M1.within.species):species

where the first term models between-species phylogentically correlated  
variation in intercepts and slopes  and the second term models  
between-species variation in intercepts and slopes that is not  
phylogenetically correlated. However, you have to be quite careful  
with the van der Pol & Wright method because measurement error in the  
species means (which will be high when n=3) can appear as random  
variation in slopes. The section "Within-Population Slope  
Heterogeneity" in this paper:

http://www.pnas.org/content/107/18/8292.full

discusses the problem, but unfortunately without a good resolution.

2/ I generally use parameter expanded priors of the form:

G2 = list(V = diag(2), nu = 2, alpha.mu = rep(0, 2), alpha.V= diag(500, 2, 2))

note V is an identity matrix rather than I*0.5. However, you should  
check to make sure you don't get big changes when you use other types  
of prior.

Cheers,

Jarrod







Quoting Alberto Gallano <alberto.gc8 at gmail.com> on Sun, 21 Dec 2014  
17:59:09 -0500:

> I have a question about prior and random effects specification for a
> phylogenetic mixed model. I am fitting a linear mixed model using MCMCglmm,
> accounting for phylogenetic dependence in the residuals. My fixed effects
> are two continuous variables (ratios of central and lateral incisor width
> to first molar length) in various species of animals (n = 106). I have
> measurements for multiple individuals within each species (ranging from n=3
> to n=110). I am mainly interested in the among-species slope and intercept.
> Therefore, I have used the methods outlined in (van der Pol & Wright, 2009)
> to split the explanatory variable into two: one with species means, the
> other within-species centered. This disentangles effects for within- and
> between species. For random effects, I am fitting random intercepts for the
> species level phylogenetic random effect (called "phylo"), random
> intercepts for the species level non-phylogenetic random effect (called
> "species"), and random slopes for the within-species centered variable.
>
> I have two questions:
>
> 1) I want to a model that allows random slopes to vary for each species,
> but i'm not sure if I have this specified correctly? Also, should the
> random slopes be coupled with the "species" or "phylo" random effect?
>
> 2) What is a good prior for the random slope / random intercept (here G2)?
> I'm not sure whether this is specified correctly (e.g., should I used
> parameter expanded priors)?
>
> Here are the priors and model:
>
> priors1 <- list(
>     B = list(mu = rep(0, 3), V = diag(9, 3)),
>     G = list(G1 = list(V = 1, nu = 0.002), G2 = list(V = diag(2)/2, nu =
> 0.002)),
>     R = list(V = 1, nu = 0.002)
>     )
>
> # parameter expanded version
> priors2 <- list(
>     B = list(mu = rep(0, 3), V = diag(9, 3)),
>     G = list(G1 = list(V = 1, nu = 0.002),
>              G2 = list(V = diag(2)/2, nu = 2, alpha.mu = rep(0, 2), alpha.V
> = diag(500, 2, 2))),
>     R = list(V = 1, nu = 0.002)
>     )
>
> # inverse of sigma matrix of phylogenetic correlation
> inv_phylo_mat <- inverseA(tree, nodes = "TIPS", scale = TRUE)
>
> fit <- MCMCglmm(
>     fixed = I1.M1 ~ I2.M1.species.mean + I2.M1.within.species,
>     rcov = ~ units,
>     random = ~ phylo + idh(1+I2.M1.within.species):species,
>     data = incisor.dat,
>     family = "gaussian",
>     ginverse = list(phylo = inv_phylo_mat$Ainv),
>     prior = priors1,
>     pr = TRUE,
>     pl = TRUE,
>     nitt = 1.1e+6, thin = 10, burnin = 1e+5,
>     verbose = FALSE
>     )
>
>
> best,
> Alberto
>
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>
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