Location: D.M. Smith Room 303
Join us for a workshop on original policy research (WOPR) featuring School of Public Policy Professor Scott Ganz, whose talk will be titled: "Goldilocks vs. Robin Hood: Using shape-constrained regression to evaluate u-shaped (or inverse u-shaped) theories in data."
Absract: Theories that predict u-shaped and inverse u-shaped relationships are ubiquitous throughout the social sciences. As a result of this widespread interest in identifying u-shaped and inverse u-shaped relationships in data and the well-known problems with standard parametric approaches based on quadratic regression models, there has been considerable recent interest in finding new ways to evaluate such theories using semi-parametric and non-parametric methods. In this paper, I propose a new method for evaluating these theories, which I call the ``Goldilocks'' algorithm. The algorithm is so named because it involves estimating three models in order to evaluate a u-shaped or inverse u-shaped hypothesis. One model is too flexible (``too hot'') because it permits multiple inflection points in the expected relationship between x and y. One is too inflexible (``too cold'') because it does not permit any inflection points. The final model (``just right'') permits exactly one inflection point. In a simulation study based on 234 monotonic-increasing or inverse u-shaped functional forms and over 100 thousand simulated datasets, I show that my proposed algorithm outperforms the current favored method for testing u-shaped and inverse u-shaped hypotheses, called the ``Robin Hood'' algorithm, in terms of controlling the false rejection rate and the power of the test.