Moving Beyond the Linear Regression Model

Abstract

Heavy-tailed distributions occur often in empirical settings, making it difficult for management scholars to use linear regression models (LRMs) to investigate the nuanced relationships between dependent and predictor variables. Both frequentist and Bayesian quantile regression models (QRMs) are alternative techniques that can help management scholars overcome the hurdles associated with using LRMs. This study compares LRMs and QRMs and shows how the frequentist and Bayesian QRM can open up doors for management scholars to develop and test theory in novel and informative ways. In introducing Bayesian estimation, it also shows how Bayesian quantile regression can achieve what existing Bayesian LRM and frequentist QRM techniques cannot. Following this exploration, this paper explains how management researchers can systematically apply QRMs in two concrete empirical settings. The first example shows that organizational behavior and human resource scholars can apply QRMs to study questions related to gender inequality. The second example illustrates that QRMs enable strategy and organizational theory researchers to detect nuanced relations between environmental factors and firm performance. This paper demonstrates that the QRM is a comprehensive strategy capable of helping researchers obtain a complete regression picture for data with heavy-tailed distributions.