Phylogenetic signal when using sratio() family

Modeling
,
1

I am modelling an ordinal (sequential) response variable with three levels as a function of four predictors using brms with an sratio() family for the response. The response variable is competence of rodents for a parasite (0 = resistant, 1 = susceptible, 2 = competent) and my training dataset comprises 77 rodent species each associated to four predictor values.

Before modelling, I have tested for phylogenetic signal in the response variable using the delta statistic developed for categorical variables (Borges et al. 2019, Bioinformatics) and I haven’t found evidence for a signal.

Nethertheless, I have incorporated phylogeny in my model to account for the non-independence of errors due to phylogenetic relatedness between species.


model  <- brm(
        Competence ~ Range.size.z + Dispersal.z
        + Body.mass.z + Diet.breadth.z + (1|gr(Species, cov = A)),
        data = Data,
        data2 = list(A = A),
        family = sratio(),
        chains = 4,
        iter = 15000,
        prior = prior1,
        init = 0,
        warmup = 1000,
        control = list(max_treedepth = 15, adapt_delta = 0.99))

However, I obtained a 0.14 estimate for the sd of the group-level effect (the phylogenetic random effect) with 0.01-0.44 95% CIs.

I’m struggling with the interpretation of this result: dealing with an ordinal variable does this result imply the presence of a phylogenetic signal? Can you help me interpret this result?

Thanks in advance for any feedback!

2

HI,

I’m also interested in this. I’ve been using the cumulative family for a phylogenetic model, and would also like to calculate the phylo signal if possible. So far I’ve only been successful with standard gaussian models, but I haven’t put much thought into try to understand the underlying process.

Hopefully someones got some good thoughts on it!

3

You can think of the species level variance as consisting of two components: one that is phylogenetically structured, and one that is unstructured. The phylogenetic signal is the fraction of the variance that is phylogenetically structured. For Gaussian models with one observation per species, the unstructured component is just the residual. For other models, you need to tell the model that you want to include an unstructured species level variance component by including a random effect of species.

This approach yields an estimate of the phylogenetic signal in the species-level expectations, but not necessarily the phylogenetic signal in the actual species-level values, since there is a third variance component, which is the sampling variance of the response distribution itself. If you believe that the response-distribution variance is a within-species variance (e.g. if it is the sampling variation across individuals within a species), then you should recover an estimate of the phylogenetic signal in the (link-scale) species means. But if you believe that the residual variance is actually variance in the true species-level mean, then the procedure outlined above will overstate the strength of the phylogenetic signal overall.

I don’t know enough about the sratio family to comment specifically on this particular case.