Treat offset accordingly

[tomicapretto]

This PR closes #528

See example

import arviz as az
import bambi as bmb
import numpy as np

data = bmb.load_data("carclaims")

model = bmb.Model("numclaims ~ offset(np.log(exposure))", data, family="poisson", link="log")
model

Formula: numclaims ~ offset(np.log(exposure))
Family name: Poisson
Link: log
Observations: 67856
Priors:
  Common-level effects
    Intercept ~ Normal(mu: 0, sigma: 2.5)

  Offset effects
    offset(np.log(exposure)) ~ 1

idata = model.fit(random_seed=1234)
az.summary(idata)

Using brms we obtain..

library(brms)

data <- read.csv("data.csv")
model <- brm(numclaims ~ offset(log(exposure)), data, family=poisson(log))
model

 Family: poisson 
  Links: mu = log 
Formula: numclaims ~ offset(log(exposure)) 
   Data: data (Number of observations: 67856) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept    -1.86      0.01    -1.89    -1.84 1.00     1475     1991

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

[tomicapretto]

Predictions using offsets require more work on our predict method... I'll work on it in the following days.

Meant to put comment as this is still in WIP

[codecov-commenter]

Codecov Report

Merging #534 (162d76a) into main (91903c8) will increase coverage by 0.08%.
The diff coverage is 90.00%.

❗ Current head 162d76a differs from pull request most recent head da74497. Consider uploading reports for the commit da74497 to get more accurate results

@@            Coverage Diff             @@
##             main     #534      +/-   ##
==========================================
+ Coverage   86.84%   86.93%   +0.08%     
==========================================
  Files          32       32              
  Lines        2622     2655      +33     
==========================================
+ Hits         2277     2308      +31     
- Misses        345      347       +2     

Impacted Files	Coverage Δ
bambi/terms.py	76.53% <66.66%> (-1.11%)	⬇️
bambi/backend/pymc.py	81.22% <100.00%> (+0.33%)	⬆️
bambi/models.py	89.75% <100.00%> (+1.09%)	⬆️
bambi/tests/test_predict.py	100.00% <100.00%> (ø)
bambi/tests/test_built_models.py	99.00% <0.00%> (-0.04%)	⬇️
bambi/utils.py	70.96% <0.00%> (+3.22%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 91903c8...da74497. Read the comment docs.

[tomicapretto]

@aloctavodia @canyon289 I would like approval before merging. I would like to check if you have any questions/concerns about how this works.

[canyon289]

These tests show that the model compiles and MCMC runs. What would be nice is a check that ensures the correct parameters are recovered as well. Not required for this PR just mentioning it

[tomicapretto]

Yeah, and this is the case for all our tests by the way. I think there's an issue for that, but we've never worked on it.

I think it's OK to merge this as it is now. We could work on tests for correctness in the future.