Bayesian Mixed Logit in PyMC Marketing
Mixed Logit Choice Models for Consumer Choice
This addition completes the core discrete-choice toolkit, sitting alongside:
- Multinomial Logit
- Nested Logit
- Mixed Logit (new)
The implementation supports:
- ✅ Individual-level preference heterogeneity via hierarchical random coefficients
- ✅ Panel data with group-level effects
- ✅ Non-centered parameterizations for better sampling
- ✅ Control-function correction for price endogeneity using instruments
- ✅ Full posterior & counterfactual simulation for policy and pricing interventions
- ✅ Wilikinson Style Formula interface
Mixed logit is the workhorse model behind modern preference estimation, WTP analysis, and market simulations — and it’s now fully Bayesian, transparent, and extensible in PyMC.
The latent utility for alternative \(j\) is
\[ U_{njt} = \underbrace{ \boldsymbol{\alpha} }_{\text{alt-specific fixed effects}} + \underbrace{ \mathbf{x}_{njt}^\top \boldsymbol{\beta}_n }_{\text{alt-specific random effects}} + \underbrace{ \mathbf{z}_{n}^\top \boldsymbol{\gamma}_j }_{\text{individual-specific effects}} + \overbrace{ \underbrace{ \mathbf{r}_{njt}^\top \boldsymbol{\lambda_{cf}} }_{\text{control function}} }^{\text{optional endogeneity correction}} + \varepsilon_{njt} \]