Dealing with Separation in Logistic Regression Models

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.

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Carlisle Rainey

January 09, 2016
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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.
  8. None
  9. None
  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.
  26. None