Carlisle Rainey
January 09, 2016
120

# 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.

January 09, 2016

## Transcript

1. Dealing with Separation in
Logistic Regression Models
Carlisle Rainey
Assistant Professor
Texas A&M University
[email protected]
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. Different default priors
produce different results.

9. The Prior Matters
in Theory

10. 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
| )
.

11. 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
| )
.

12. The prior determines
crucial parts of the posterior.

13. Key Concepts
for Choosing a Good Prior

14. Pr
(
yi) = ⇤( c + ssi + 1xi1 +
...
+ kxik)

15. Transforming the Prior
Distribution
˜ ⇠ p( )
˜
⇡new = p(ynew
|˜)
˜
qnew = q(˜
⇡new)

16. We Already Know Few Things
1
⇡ ˆmle
1
2
⇡ ˆmle
2
.
.
.
k
⇡ ˆmle
k
s < 0

17. Partial Prior Distribution
p⇤( | s < 0, s = ˆmle
s
),
where ˆmle
s
= 1

18. The Pacifying Effects of Nuclear Weapons

19. Software
for Choosing a Good Prior

20. separation
(on GitHub)

21. Conclusion

22. The prior matters a lot,
so choose a good one.

23. 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.