BIC extensions for order-constrained model selection

TL;DR

This paper introduces two extensions of the BIC for better evaluation of models with order constraints, demonstrating improved accuracy and practical implementation in R for social science research.

Contribution

It proposes and compares two BIC extensions for order-constrained models, with the local unit information prior showing superior performance and providing an R package for easy application.

Findings

The local unit information prior-based BIC outperforms other methods in model selection accuracy.

The methodology reduces error probabilities in evaluating order-constrained models.

The approach is practically implemented in the R package `BICpack' and demonstrated with real data.

Abstract

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of interest. This paper explores two extensions of the BIC for evaluating order constrained models, one where a truncated unit information prior is used under the order-constrained model, and the other where a truncated local unit information prior is used. The first prior is centered around the maximum likelihood estimate and the latter prior is centered around a null value. Several analyses show that the order-constrained BIC based on the local unit information prior works better as an Occam's razor for evaluating order-constrained models and results in lower error probabilities. The methodology based on the local unit information prior is implemented in the R package `BICpack' which allows researchers to easily apply the method for order-constrained model selection. The usefulness of the methodology is illustrated using data from the European Values Study.