Exploring curvilinearity through fractional polynomials in management research
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Date
2015
Authors
Nikolaeva, Ralitza
Bhatnagar, Amit
Ghose, Sanjoy
Journal Title
Journal ISSN
Volume Title
Publisher
Organizational Research Methods, Forthcoming
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.
Description
Keywords
fractional polynomials, curvilinear relationships, non-monotonic curves, abductive method