Exploring curvilinearity through fractional polynomials in management research

Abstract

Imprecise theories do not give enough guidelines for empirical analyses. A paradigmatic shift from linear to curvilinear relationships is necessary to advance management theories. Within the framework of the abductive generation of theories, the authors present a data exploratory technique for the identification of functional relationships between variables. Originating in medical research, the method uses fractional polynomials to test for alternative curvilinear relationships. It is a compromise between nonparametric curve fitting and conventional polynomials. The multivariable fractional polynomial (MFP) technique is a good tool for exploratory research when theoretical knowledge is nonspecific and thus very useful in phenomena discovery. The authors conduct simulations to demonstrate MFP’s performance in various scenarios. The technique’s major benefit is the uncovering of nontraditional shapes that cannot be modeled by logarithmic or quadratic functions. While MFP is not suitable for small samples, there does not seem to be a downside of overfitting the data as the fitted curves are very close to the true ones. The authors call for a routine application of the procedure in exploratory studies involving medium to large sample sizes.