INLA for distributional regression (predictors on parameters of distributions)

[eby]

Dear INLA users,

I am trying to fit distributional regression models with INLA (regression models similar to gamlss, i.e., generalized additive models on the parameters of a distribution rather on its mean), but I cannot find appropriate resources on the help page.

I've come across the paper (below) which states in page 1073 that distributional regression is not supported by INLA. Is this still true (if it was)? If not, how could I fit a model, for example gaussian model, with one gam on the mean and another on the standard deviation and get their corresponding fitted values, please? The vignette for gaussian models includes an example for mu only (not tau). The question is not restricted to gaussian models and could be equally valid for any distribution with more than 1 parameter.

Example

y_i ~ F(mu_i, tau_i, xi_i), where F depends upon covariates x1, ..., x6, through

mu_i = f1(x1) + f2(x2) + ...,

tau_i = f3(x3) + f4(x4) + ...,

xi_i = f5(x5) + f6(x6) + ...

I would expect something like

formula = y~f(x1, model="rw2") + f(x2, model="rw2"), how to include those for tau and xi?

fit <- inla(formula, data=data, control.predictor=list(compute=TRUE))

mu <- fit$summary.fitted.values[...]

tau <- fit$summary.fitted.values[...]

...

Thanks for your help!

Klein, N., Kneib, T. et al. (2016). Scale-Dependent Priors for Variance Parameters in Struc- tured Additive Distributional Regression. Bayesian Analysis 11 1071–1106. https://projecteuclid.org/download/pdfview_1/euclid.ba/1448323525

[Finn Lindgren]

Hi,

The inlabru package is intended to be able to handle some such models. A parametric distribution model is part of the tutorials linked on inlabru.org (spatially dependent animal group size distribution), but nonparametric versions is just a matter of including such components in the model definition, like you describe. The main idea is that inlabru allows the user to specify fairly general R expressions, which allows the model components to enter in places where inla cannot have them. What we’ve done so far involves point process formulations of the problem. We’re working on generalizing and working out properties of the method, so we haven’t published the specifics on distribution estimation with this approach yet.

Finn

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[Yousra El Bachir]

Thanks for your prompt reply. I'll keep an eye on the package then...

Finn

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