A Default Prior Distribution for Logistic and Other Regression Models
22 Pages Posted: 11 Sep 2007
Date Written: August 3, 2007
Abstract
We propose a new prior distribution for classical (non-hierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-t prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. We implement a procedure to fit generalized linear models in R with this prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several examples, including a series of logistic regressions predicting voting preferences, an imputation model for a public health data set, and a hierarchical logistic regression in epidemiology. We recommend this default prior distribution for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small) and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation.
Keywords: Bayesian inference, generalized linear model, least squares, hierarchical model, linear regression, logistic regression, multilevel model, noninformative prior distribution
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Untangling the Causal Effects of Sex on Judging
By Christina L. Boyd, Lee Epstein, ...
-
By Lee Epstein and Gary King
-
By Adam B. Cox and Thomas J. Miles
-
Decision-Making Under a Norm of Consensus: A Structural Analysis of Three-Judge Panels
-
Strategic Judicial Lawmaking: Ideology, Publication, and Asylum Law in the Ninth Circuit
By David S. Law
-
Do Judges Make Regulatory Policy?: An Empirical Investigation of Chevron
By Thomas J. Miles and Cass R. Sunstein
-
Do Judges Make Regulatory Policy? An Empirical Investigation of 'Chevron'
By Thomas J. Miles and Cass R. Sunstein
-
Judicial Hostility Toward Labor Unions? Applying the Social Background Model to a Celebrated Concern
By James J. Brudney, Sara Schiavoni, ...
-
What Is Judicial Ideology, and How Should We Measure It?
By Joshua B. Fischman and David S. Law