Bias reduction, the Jeffreys prior and GLIM

Summary

In full exponential-family models, such as generalized linear models with canonical link, use of the Jeffreys invariant prior as a penalty function removes the leading term from the asymptotic bias of maximum likelihood estimates. In Poisson log linear and binomial logistic linear models, the posterior mode can be calculated using the standard iterative weighted least-squares algorithm with an appropriate adjustment to the working vector at each cycle. The required adjustment is a simple function of case leverages. Implementation is particularly straightforward in GLIM4, and illustrates the power of the new ‘OWN algorithm’ facility.