Bayesian decision theory for tree-based adaptive screening tests with an application to youth delinquency

Abstract

Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high-risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they should also be reasonably brief; adaptive screening tests are useful for this purpose. Adaptive tests constructed using classification and regression trees are becoming a popular alternative to traditional item response theory (IRT) approaches for adaptive testing. However, tree-based adaptive tests lack a principled criterion for terminating the test. This paper develops a Bayesian decision theory framework for measuring the trade-off between brevity and accuracy when considering tree-based adaptive screening tests of different lengths. We also present a novel method for designing tree-based adaptive tests, motivated by this framework. The framework and associated adaptive test method are demonstrated through an application to youth delinquency risk assessment in Honduras; it is shown that an adaptive test requiring a subject to answer fewer than 10 questions can identify high-risk youth nearly as accurately as an unabridged survey containing 173 items.