Bayesian Kinked Regression with Unobserved Thresholds: An Application to the von Liebig Hypothesis

Abstract

We consider the Bayesian estimation of continuous regression models where the cutoff points that separate different slope regimes are unknown but related to an observed input. Using plateau and von Liebig production functions as examples, we compare the performance of Bayesian mixture models that explicitly estimate regime membership probabilities to Bayesian threshold models that instead treat the unobserved threshold input as a model parameter. Using simulated data as well as actual data from two crop response trials, we show that the threshold model generally outperforms the mixture model in terms of estimation efficiency and predictive accuracy. We also illustrate how Bayesian model averaging can be employed when model performance is less clear cut. Our estimation framework is suitable for a wide range of applications in agricultural and resource economics —as well as other fields.