Model selection via Bayesian information capacity designs for generalised linear models

TL;DR

This paper introduces a Bayesian information capacity criterion for selecting robust experimental designs in generalized linear models, demonstrating effective screening for binomial and Poisson data through simulation studies.

Contribution

It proposes a new Bayesian criterion for design selection in generalized linear models, enhancing robustness and screening efficiency.

Findings

Designs achieve high power with moderate error rates

Logistic regression is more challenging than log-linear regression

Effective screening depends on support points and experiment size

Abstract

The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are robust to the form of the linear predictor. For binomial data and logistic regression, the effectiveness of these designs for screening is assessed through simulation studies using all-subsets regression and model selection via maximum penalised likelihood and a generalised information criterion. For Poisson data and log-linear regression, similar assessments are made using maximum likelihood and the Akaike information criterion for minimally-supported designs that are constructed analytically. The results show that effective screening, that is, high power with moderate type I error rate and false discovery rate, can be achieved through suitable choices for the number of design support points and experiment size. Logistic regression is shown to present a more challenging problem than log-linear regression. Some areas for future work are also indicated.