On the small sample properties of norm-restricted maximum likelihood estimators for logistic regression models

1989 ◽  
Vol 18 (3) ◽  
pp. 959-980 ◽  
Author(s):  
Diane E. Duffy ◽  
Thomas J. Santner
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Regression Models ◽  
Maximum Likelihood Estimators ◽  
Restricted Maximum Likelihood ◽  
Small Sample ◽  
Logistic Regression Models ◽  
Small Sample Properties

Dealing with Separation in Logistic Regression Models

2016 ◽  
Vol 24 (3) ◽  
pp. 339-355 ◽  
Author(s):  
Carlisle Rainey
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Prior Distribution ◽  
Regression Models ◽  
Prior Information ◽  
Jeffreys Prior ◽  
Logistic Regression Models ◽  
Explanatory Variables ◽  
Point Estimates ◽  
Quantities Of Interest

When facing small numbers of observations or rare events, political scientists often encounter separation, in which explanatory variables perfectly predict binary events or nonevents. In this situation, maximum likelihood provides implausible estimates and the researcher might want incorporate some form of prior information into the model. The most sophisticated research uses Jeffreys’ invariant prior to stabilize the estimates. While Jeffreys’ prior has the advantage of being automatic, I show that it often provides too much prior information, producing smaller point estimates and narrower confidence intervals than even highly skeptical priors. To help researchers assess the amount of information injected by the prior distribution, I introduce the concept of a partial prior distribution and develop the tools required to compute the partial prior distribution of quantities of interest, estimate the subsequent model, and summarize the results.

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