A Primer on Bayesian Methods for Multilevel Modeling

Abstraction: Bayesian hierarchical modeling with PyMC3 using partial pooling

Key points:

• Multilevel models allow parameters to vary by group; hierarchical models nest parameters within one another
• Complete pooling (single estimate) vs. no pooling (independent estimates) represent the bias-variance tradeoff extremes; partial pooling is the multilevel compromise
• Partial pooling estimate is approximately a weighted average of unpooled county estimates and pooled state estimate, weighted by sample size
• Demonstrates varying-intercept, varying-slope, and varying-intercept-plus-slope models on EPA radon dataset (80,000 houses, Minnesota)
• Floor coefficient estimate: approximately -0.66, meaning houses without basements have ~52% the radon levels of those with basements
• Cross-validation RMSE: unpooled=0.86, pooled=0.84, multilevel=0.79; uses PyMC3 with NUTS sampler

Connections: Pymc · Bayesian Inference · Multilevel Modeling · Markov Chain Monte Carlo · Hierarchical Models

Source: http://nbviewer.ipython.org/github/fonnesbeck/multilevel_modeling/blob/master/multilevel_modeling.ipynb