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

Area of Science:

• Bibliometrics
• Scientific Productivity
• Statistical Modeling

Background:

• The equal odds baseline model posits a linear relationship between total and high-quality scientific works, with no correlation between their proportions.
• The tilted funnel hypothesis suggests this relationship is heteroscedastic, with increasing variance in work quality as quantity rises.

Purpose of the Study:

• To apply Bayesian statistical modeling to the equal odds baseline model of creative scientific productivity.
• To investigate the tilted funnel hypothesis using advanced Bayesian techniques beyond traditional frequentist methods.

Main Methods:

• Leveraging Bayesian statistical modeling, including Poisson modeling, to analyze conditional variance as a function of quantity.
• Utilizing the brms Bayesian R package and a small dataset of eminent neurosurgeons.
• Developing novel Bayesian methods to address limitations of existing frequentist quantile regression.

Main Results:

• The study provides a Bayesian framework for analyzing the relationship between scientific output quantity and quality.
• Demonstrates the utility of Bayesian Poisson modeling for assessing heteroscedasticity in scientific productivity.
• Offers open-access code and data for reproducible research and further exploration.

Conclusions:

• Bayesian modeling offers a flexible approach to understanding the nuances of scientific productivity beyond simple linear assumptions.
• The findings support the tilted funnel hypothesis, indicating that the variance in scientific work quality increases with the quantity of output.
• The proposed methods and open data facilitate future research into the complex dynamics of scientific creativity.