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 non-parametric curve fitting and conventional polynomials. The multivariable fractional polynomial (MFP) technique is a good tool for exploratory research when theoretical knowledge is non-specific 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 non-traditional 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 and large sample sizes.