Unclear what posterior parameter relates to what formula predictor

[rikhuijzer]

Currently, the posterior parameters have the form β[1], ..., β[n] whereas formulas used something along the lines of y ~ a + b + c. This is now tricky to link again because I don't know without looking into the code what parameter belongs to what predictor.

[rikhuijzer]

I've been thinking about a possible solution. We probably could add methods for sample which take a GLMModel. For example,

import Turing: sample

using MCMCChains: replacenames

struct GLMModel
    model::DynamicPPL.Model
    name_mapping::Dict{String,String}
end

function sample(gm::GLMModel, sampler, n_samples)
    chns = sample(gm.model, sampler, n_samples)
    updated_chns = replacenames(chns, gm.name_mapping)
    return updated_chns
end

# And more additional methods for `sample`
[...]

From the user-side, things wouldn't change so much. In most cases, it would still be:

fm = @formula(...)
model = turing_model(fm, data)
chns = sample(model, NUTS(), 2_000)

[phipsgabler]

Just loading off a random idea here, but what about keeping the predictor names in β itself? E.g., a NamedArrays.jl solution:

julia> β = NamedArray(rand(3), ["a", "b", "c"], "Predictor")
3-element Named Vector{Float64}
Predictor  │ 
───────────┼─────────
a          │ 0.143747
b          │ 0.253579
c          │ 0.143526

[kleinschmidt]

Ideally we can build something on top of coefnames(::AbstractTerm) which can do that substitution for you, although it might be a bit tricky since it looks like the intercept column is manually removed during construction.

[storopoli]

Yes, a coefnames would be great.
Intercept is always \alpha. It was removed because brms constructs the model as fast as possible for a MCMC NUTS sampler and this involves not using the 1 or 0 column in the model matrix.

[storopoli]

We could do the same thing we do with the idx for random-intercept:

julia> using TuringGLM

julia> cheese = CSV.read(download("https://github.com/TuringLang/TuringGLM.jl/raw/main/data/cheese.csv"), DataFrame);

julia> f = @formula(y ~ (1 | cheese) + background);

julia> m = turing_model(f, cheese);
The idx are Dict{String1, Int64}("B" => 2, "A" => 1, "C" => 3, "D" => 4)