ENH: support logit random coefficients

pyblp/economies/economy.py

@@ -110,8 +110,8 @@ def __init__(
                 raise TypeError("rc_types must be None or a sequence.")
             if len(rc_types) != self.K2:
                 raise ValueError(f"rc_types must be None or a sequence of length {self.K2}.")
-            if any(d not in {'linear', 'log'} for d in rc_types):
-                raise TypeError("rc_types must be None or a sequence of 'linear' or 'log' strings.")
+            if any(d not in {'linear', 'log', 'logit'} for d in rc_types):
+                raise TypeError("rc_types must be None or a sequence of 'linear', 'log', or 'logit' strings.")
             self.rc_types = list(rc_types)
 
         # validate the scale of epsilon

pyblp/economies/problem.py

@@ -1348,7 +1348,11 @@ class Problem(ProblemEconomy):
             - ``'linear'`` (default) - The random coefficient is as defined in :eq:`mu`.
 
             - ``'log'`` - The random coefficient's column in :eq:`mu` is exponentiated before being pre-multiplied by
-              :math:`X_2`.
+              :math:`X_2`. It will take on values bounded from below by zero.
+
+            - ``'logit'`` - The random coefficient's column in :eq:`mu` is passed through the inverse logit function
+              before being pre-multiplied by :math:`X_2`. It will take on values bounded from below by zero and above by
+              one.
 
         The list should have as many strings as there are columns in :math:`X_2`. Each string determines the type of the
         random coefficient on the corresponding product characteristic in :math:`X_2`.

pyblp/economies/simulation.py

@@ -218,7 +218,11 @@ class Simulation(Economy):
             - ``'linear'`` (default) - The random coefficient is as defined in :eq:`mu`.
 
             - ``'log'`` - The random coefficient's column in :eq:`mu` is exponentiated before being pre-multiplied by
-              :math:`X_2`.
+              :math:`X_2`. It will take on values bounded from below by zero.
+
+            - ``'logit'`` - The random coefficient's column in :eq:`mu` is passed through the inverse logit function
+              before being pre-multiplied by :math:`X_2`. It will take on values bounded from below by zero and above by
+              one.
 
         The list should have as many strings as there are columns in :math:`X_2`. Each string determines the type of the
         random coefficient on the corresponding product characteristic in :math:`X_2`.

pyblp/markets/market.py

@@ -4,6 +4,7 @@
 from typing import Any, Dict, Iterator, List, Optional, Tuple
 
 import numpy as np
+import scipy.special
 
 from .. import exceptions, options
 from ..configurations.iteration import ContractionResults, Iteration
@@ -167,6 +168,14 @@ def compute_random_coefficients(self, sigma: Optional[Array] = None, pi: Optiona
                 else:
                     assert len(coefficients.shape) == 3
                     coefficients[:, k] = np.exp(coefficients[:, k])
+            elif rc_type == 'logit':
+                if len(coefficients.shape) == 2:
+                    coefficients[k] = scipy.special.expit(coefficients[k])
+                else:
+                    assert len(coefficients.shape) == 3
+                    coefficients[:, k] = scipy.special.expit(coefficients[:, k])
+            else:
+                assert rc_type == 'linear'
 
         return coefficients
 
@@ -180,6 +189,10 @@ def compute_single_random_coefficient(self, k: int) -> Array:
 
         if self.parameters.rc_types[k] == 'log':
             coefficient = np.exp(coefficient)
+        elif self.parameters.rc_types[k] == 'logit':
+            coefficient = scipy.special.expit(coefficient)
+        else:
+            assert self.parameters.rc_types[k] == 'linear'
 
         return coefficient
 
@@ -856,6 +869,12 @@ def compute_utility_derivatives_by_parameter_tangent(
             v = parameter.get_agent_characteristic(self)
             if parameter.get_rc_type(self) == 'log':
                 v = v * self.compute_single_random_coefficient(parameter.location[0]).T
+            elif parameter.get_rc_type(self) == 'logit':
+                rc = self.compute_single_random_coefficient(parameter.location[0]).T
+                v = v * rc * (1 - rc)
+            else:
+                assert parameter.get_rc_type(self) == 'linear'
+
             tangent += X2_derivatives[:, [parameter.location[0]]] * v.T
         else:
             assert isinstance(parameter, (GammaParameter, RhoParameter))
@@ -939,6 +958,12 @@ def compute_probabilities_by_parameter_tangent(
                 v = parameter.get_agent_characteristic(self)
                 if parameter.get_rc_type(self) == 'log':
                     v = v * self.compute_single_random_coefficient(parameter.location[0]).T
+                elif parameter.get_rc_type(self) == 'logit':
+                    rc = self.compute_single_random_coefficient(parameter.location[0]).T
+                    v = v * rc * (1 - rc)
+                else:
+                    assert parameter.get_rc_type(self) == 'linear'
+
                 probabilities_tangent = probabilities * v.T * (x - x.T @ probabilities)
             else:
                 assert isinstance(parameter, GammaParameter)
@@ -970,6 +995,11 @@ def compute_probabilities_by_parameter_tangent(
             v = parameter.get_agent_characteristic(self)
             if parameter.get_rc_type(self) == 'log':
                 v = v * self.compute_single_random_coefficient(parameter.location[0]).T
+            elif parameter.get_rc_type(self) == 'logit':
+                rc = self.compute_single_random_coefficient(parameter.location[0]).T
+                v = v * rc * (1 - rc)
+            else:
+                assert parameter.get_rc_type(self) == 'linear'
 
             # compute the tangent of conditional probabilities with respect to the parameter
             vx = v.T * x

tests/conftest.py

@@ -524,7 +524,7 @@ def large_nested_blp_simulation() -> SimulationFixture:
         xi_variance=0.00001,
         omega_variance=0.00001,
         correlation=0.9,
-        rc_types=['log', 'linear'],
+        rc_types=['log', 'logit'],
         costs_type='log',
         seed=0,
     )