Adding default priors for Binomial/Bernoulli families with logit link

.gitignore

@@ -20,3 +20,5 @@ docs/_build
 pytest.ini
 /.quarto/
 .Rproj.user
+# Git ignore all the notebook files in the root
+*.ipynb

bambi/priors/scaler.py

@@ -1,7 +1,15 @@
 import numpy as np
 import pymc as pm
 
-from bambi.families.univariate import Cumulative, Gaussian, StoppingRatio, StudentT, VonMises
+from bambi.families.univariate import (
+    Bernoulli,
+    Binomial,
+    Cumulative,
+    Gaussian,
+    StoppingRatio,
+    StudentT,
+    VonMises,
+)
 from bambi.model_components import ConstantComponent
 from bambi.priors.prior import Prior
 
@@ -30,8 +38,7 @@ def __init__(self, model):
     def get_intercept_stats(self):
         mu = self.response_mean
         sigma = self.STD * self.response_std
-
-        # Only adjust mu and sigma if there is at least one Normal prior for a common term.
+        # Only adjust sigma if there is at least one Normal prior for a common term.
         if self.priors:
             sigmas = np.hstack([prior["sigma"] for prior in self.priors.values()])
             x_mean = np.hstack(
@@ -58,23 +65,73 @@ def scale_response(self):
     def scale_intercept(self, term):
         if term.prior.name != "Normal":
             return
-        mu, sigma = self.get_intercept_stats()
+        # Special case for logit/probit links with bernoulli or binomial family
+        if isinstance(self.model.family, (Bernoulli, Binomial)) and self.model.family.link[
+            "p"
+        ].name in ["logit", "probit"]:
+            mu = 0
+            sigma = 1.5
+        else:
+            mu, sigma = self.get_intercept_stats()
         term.prior.update(mu=mu, sigma=sigma)
 
     def scale_common(self, term):
         if term.prior.name != "Normal":
             return
 
-        # It can be greater than 1 for categorical variables
         if term.data.ndim == 1:
             mu = 0
-            sigma = self.get_slope_sigma(term.data)
+            # Special case for logit/probit links with bernoulli or binomial family
+            if isinstance(self.model.family, (Bernoulli, Binomial)) and self.model.family.link[
+                "p"
+            ].name in ["logit", "probit"]:
+                # For interaction terms, distinguish cases where all factor terms are categorical
+                if term.kind == "interaction":
+                    all_categoric = all(
+                        component.kind == "categoric" for component in term.term.components
+                    )
+                    if all_categoric:
+                        sigma = 1
+                    else:
+                        sigma = 1 / np.std(term.data, axis=0)
+                # Single categorical term
+                elif term.categorical:
+                    sigma = 1
+                # Single numerical term
+                else:
+                    sigma = 1 / np.std(term.data, axis=0)
+            # If not, fall back to the regular case
+            else:
+                sigma = self.get_slope_sigma(term.data)
+        # It's a term that spans multiple columns of the design matrix
         else:
             mu = np.zeros(term.data.shape[1])
             sigma = np.zeros(term.data.shape[1])
-            # Iterate over columns in the data
-            for i, value in enumerate(term.data.T):
-                sigma[i] = self.get_slope_sigma(value)
+            # Special case for logit/probit links with bernoulli or binomial family
+            if isinstance(self.model.family, (Bernoulli, Binomial)) and self.model.family.link[
+                "p"
+            ].name in ["logit", "probit"]:
+                # Iterate over columns in the data
+                for i, value in enumerate(term.data.T):
+                    if term.kind == "interaction":
+                        # Distinguish cases where all interaction factor terms are categorical
+                        all_categoric = all(
+                            component.kind == "categoric" for component in term.term.components
+                        )
+                        if all_categoric:
+                            sigma[i] = 1
+                        # It's the std dev of the marginal numerical variable (_not_ by group)
+                        else:
+                            sigma[i] = 1 / np.std(np.sum(term.data, axis=1))
+                    # Single categorical term
+                    elif term.categorical:
+                        sigma[i] = 1
+                    # Single numerical term
+                    else:
+                        sigma[i] = 1 / np.std(term.data, axis=0)
+            else:
+                for i, value in enumerate(term.data.T):
+                    sigma[i] = self.get_slope_sigma(value)
 
         # Save and set prior
         self.priors.update({term.name: {"mu": mu, "sigma": sigma}})