Correlated grouping term in a random slope model

[Thomas F Johnson]

I need to account for known correlations between a grouping term in a random slope model

Ignoring the known correlations, I can fit a model like so:

inla(y ~ 1 + f(time, species, model = "ar1"), data = dat)

where, assuming I'm right (?), I've fit different slopes for the temporal term 'time' within each of the grouping terms (species), accounting for the first-order autoregressive process.

However, as species are evolutionarily linked, with varying relation (correlation) to one another, I also need to account for the similarity in the slopes depending on the species relatedness. Something like:

inla(y ~ 1 + f(time, species, model1 = "ar1", model2 = "generic0", Cmatrix = precision_matrix), data = dat)

where the model1 term accounts for the autoregressive process of time, whilst model2 and Cmatrix account for the correlation of slopes between species.

Is anything like this possible?

[Helpdesk]

On Mon, 2021-06-07 at 08:51 -0700, Thomas F Johnson wrote:
> I need to account for known correlations between a grouping term in a
> random slope model
>
> Ignoring the known correlations, I can fit a model like so:
> inla(y ~ 1 + f(time, species, model = "ar1"), data = dat)
> where, assuming I'm right (?), I've fit different slopes for the
> temporal term 'time' within each of the grouping terms (species),
> accounting for the first-order autoregressive process.

I'm not sure if you describe this

f(time, model="ar1", replicate=species)

this will give for each 'species', an AR1 in time, wheras the above on,
gives ONE AR1 in time multiplied with species.

[I assume species is numeric 1,2,3 (or as.numeric() if its a factor) ]

>
> However, as species are evolutionarily linked, with varying relation
> (correlation) to one another, I also need to account for the
> similarity in the slopes depending on the species relatedness.
> Something like:
> inla(y ~ 1 + f(time, species, model1 = "ar1", model2 = "generic0",
> Cmatrix = precision_matrix), data = dat)
> where the model1 term accounts for the autoregressive process of time,
> whilst model2 and Cmatrix account for the correlation of slopes
> between species.

depends on 'how many' species' you have

let me know, to many loose ends right now
--
Håvard Rue
he...@r-inla.org

[Thomas F Johnson]

> I'm not sure if you describe this
> 
>   f(time, model="ar1", replicate=species)
> 
>   this will give for each 'species', an AR1 in time, wheras the above on,
>   gives ONE AR1 in time multiplied with species.
> 
>   [I assume species is numeric 1,2,3 (or as.numeric() if its a factor) ]

Okay, awesome, that makes sense. I haven't seen the replicate option is use before. Thank you. And yes, species is in an integer (that corresponds to a factor)

>   depends on 'how many' species' you have
>   
>     let me know, to many loose ends right now

There could be anywhere from 10 - 10,000 species (perhaps a median of 50), and the correlation matrix simply describes how far each species is from each other on a phylogenetic tree, similar to a distance matrix when working in space.

The overall goal is to try and account for the temporal and phylogenetic autocorrelation within timeseries

Tom

[Helpdesk]

Then I guess you're after either

f(time, model="ar1", group=species, 
control.group=list(model="besag" graph="species.graph"))

or the other way around

f(species, model="besag", graph="species.graph", group=time,
control.group=list(model="ar1"))

depending on, if there are constraints over 'species' or not.

[Helpdesk]

so the phylogenetic tree will be reflected in the graph. if you're after
spesific weights, you'll need to use model='generic' (and then the
second variant)

[Thomas F Johnson]

Amazing, thank you for the rapid and excellent support!