Dealing with Separation in Logistic Regression Models

Presented on January 9 at the 2016 Annual Meeting of the Southern Political Science Association in San Juan, Puerto Rico.

Transcript

1. Dealing with Separation in Logistic Regression Models Carlisle Rainey Assistant Professor Texas A&M University crainey@tamu.edu paper, data, and code at crain.co/research
2. The prior matters a lot, so choose a good one.
3. The prior matters a lot, so choose a good one. 1. in practice 2. in theory 3. concepts 4. software
4. The Prior Matters in Practice
5. politics need
6. Variable Coefficient Confidence Interval Democratic Governor -26.35 [-126,979.03; 126,926.33] % Uninsured (Std.) 0.92 [-3.46; 5.30] % Favorable to ACA 0.01 [-0.17; 0.18] GOP Legislature 2.43 [-0.47; 5.33] Fiscal Health 0.00 [-0.02; 0.02] Medicaid Multiplier -0.32 [-2.45; 1.80] % Non-white 0.05 [-0.12; 0.21] % Metropolitan -0.08 [-0.17; 0.02] Constant 2.58 [-7.02; 12.18]
7. Variable Coefficient Confidence Interval Democratic Governor -26.35 [-126,979.03; 126,926.33] % Uninsured (Std.) 0.92 [-3.46; 5.30] % Favorable to ACA 0.01 [-0.17; 0.18] GOP Legislature 2.43 [-0.47; 5.33] Fiscal Health 0.00 [-0.02; 0.02] Medicaid Multiplier -0.32 [-2.45; 1.80] % Non-white 0.05 [-0.12; 0.21] % Metropolitan -0.08 [-0.17; 0.02] Constant 2.58 [-7.02; 12.18] This is a failure of maximum likelihood.
10. Different default priors produce different results.
11. The Prior Matters in Theory
12. For 1. a monotonic likelihood p(y| ) decreasing in s, 2. a proper prior distribution p( | ) , and 3. a large, negative s, the posterior distribution of s is proportional to the prior distribution for s, so that p( s |y) / p( s | ) .
13. For 1. a monotonic likelihood p(y| ) decreasing in s, 2. a proper prior distribution p( | ) , and 3. a large, negative s, the posterior distribution of s is proportional to the prior distribution for s, so that p( s |y) / p( s | ) .
14. The prior determines crucial parts of the posterior.
15. Key Concepts for Choosing a Good Prior
16. Pr ( yi) = ⇤( c + ssi + 1xi1 + ... + kxik)
17. Transforming the Prior Distribution ˜ ⇠ p( ) ˜ ⇡new = p(ynew |˜) ˜ qnew = q(˜ ⇡new)
18. We Already Know Few Things 1 ⇡ ˆmle 1 2 ⇡ ˆmle 2 . . . k ⇡ ˆmle k s < 0
19. Partial Prior Distribution p⇤( | s < 0, s = ˆmle s ), where ˆmle s = 1
20. The Pacifying Effects of Nuclear Weapons
21. Software for Choosing a Good Prior
22. separation (on GitHub)
23. Conclusion
24. The prior matters a lot, so choose a good one.
25. What should you do? 1. Notice the problem and do something. 2. Recognize the the prior affects the inferences and choose a good one. 3. Assess the robustness of your conclusions to a range of prior distributions.