Distributed lag non-linear model

Modeling
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Does anyone here have experience with distributed lag non-linear models in Stan or brms (successful or not)?

Is it feasible in Stan? Existing papers use INLA or similar. And the literature we manage to find on this type of model is of a technical level that is beyond me. Tips for more introductory resources are welcome!

EDIT: brief description of DLNMs, quoting the cited abstract above:

"[…], a modelling framework that can simultaneously represent non-linear exposure-response dependencies and delayed effects. This methodology is based on the definition of a ‘cross-basis’, a bi-dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. "

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Most of the models that can be fit in INLA can also be fit in Stan. I would say if you have models that can be fit in INLA, you should use INLA. Otherwise, Stan’s a good option for more general models.

In your particular case of distributed lag models, it’s just going to be a matter of writing down the density from the paper and then translating to Stan. I don’t see a clean presentation of the full model anywhere in that paper. Like most stats papers, it starts simple with formula (1) then continues to tinker with the model without ever recapituting the final model. Maybe they have code somewhere. The R code in the paper is just a wrapper to call something doing the real work.

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