Quantity and Quality in Scientific Productivity: The Tilted Funnel Goes Bayesian

The equal odds baseline model of creative scientific productivity proposes that the number of high-quality works depends linearly on the number of total works. In addition, the equal odds baseline implies that the percentage of high-quality works and total number of works are uncorrelated. The tilted funnel hypothesis proposes that the linear regression implied by the equal odds baseline is heteroscedastic with residual variance in the quality of work increasing as a function of quantity. The aim of the current research is to leverage Bayesian statistical modeling of the equal odds baseline. Previous work has examined the tilted funnel by means of frequentist quantile regression, but Bayesian quantile regression based on the asymmetric Laplace model allows for only one conditional quantile at a time. Hence, we propose additional Bayesian methods, including Poisson modeling to study conditional variance as a function of quantity. We use a classical small sample of eminent neurosurgeons, as well as the brms Bayesian R package, to accomplish this work. In addition, we provide open code and data to allow interested researchers to extend our work and utilize the proposed modeling alternatives.