이차곡선 관계에 관한 검증방법 및 절차에 대한 제언

Since several critical issues with the existing practice used to test for U- and inverted U-shaped relationships has been identified, Lind and Mehlum (2010) proposed a three-step testing procedure. Based on the three-step procedure proposed by Lind and Mehlum (2010), the present study thoroughly reviewed current practice in business research with regard to the full procedure to testing for U- and inverted U-shaped relationships. By reviewing a set of 24 relevant articles published in Journal of Strategic Management and Korean management review from 2010 to 2022, we found some cases where there is a lack of evidence for the inverted U-shaped relationship or that lead to misleading result interpretation caused by incorrect turning point estimation. Our further simulations reveal that Lind and Mehlum's procedure also has a problem because quadratic regression always assumes a quadratic functional form when the true relationship between x and y is not quadratic(e.g. logarithmic), thereby elevating the rates of false-positive results in testing for inverted U shapes. Therefore, this study proposed a procedure that can help identify inverted U-shaped relationships more accurately in various nonlinear relationships by obtaining an accurate turning point first based on exploratory data analysis and then estimating a linear regression lines for each of the two regions separated by the turning point. The results of the study can provide both academic and practical guidelines for investigating nonlinear relationships between variables necessary to explain theories and phenomena in the he field of management and economy.