Abstract
Regression analyses reported in the applied research literature commonly assume that relationships are linear in predictors without assessing this assumption. Fractional polynomials provide a general approach for addressing nonlinearity through power transforms of predictors using real valued powers. An adaptive approach for generating fractional polynomial models is presented based on heuristic search through alternative power transforms of predictors guided by k-fold likelihood cross-validation (LCV) scores and controlled by tolerance parameters indicating how much a reduction in the LCV score can be tolerated at given stages of the search. The search optionally can generate geometric combinations, that is, products of power transforms of multiple predictors, thereby supporting nonlinear moderation analyses. Positive valued continuous outcomes can be power transformed as well as predictors. These methods are demonstrated using data from a study of family management for mothers of children with chronic physical conditions. The example analyses demonstrate that power transformation of a predictor may be required to identify that a relationship holds between that predictor and an outcome (dependent or response) variable. Consideration of geometric combinations can identify moderation effects not identifiable using linear relationships or power transforms of interactions. Power transformation of positive valued continuous outcomes along with their primary predictors can resolve model assumption problems.
Highlights
Regression analyses reported in the applied research literature commonly assume that relationships are linear in predictors without assessing this assumption
An adaptive approach for generating fractional polynomial models is presented based on heuristic search through alternative power transforms of predictors guided by k-fold likelihood cross-validation (LCV) scores and controlled by tolerance parameters indicating how much a reduction in the LCV score can be tolerated at given stages of the search
They proposed consideration of finite sets of powers. They recommended the eight powers −2, −1, −0.5, 0, 0.5, 1, 2, 3 for degree 1 fractional polynomials based on a single power transform
Summary
Regression analyses reported in the applied research literature commonly assume that relationships are linear in predictors without assessing this assumption. For this reason, Royston and Altman [1] proposed addressing nonlinearity with fractional polynomials based on power transforms of predictors using real valued powers. Royston and Altman [1] proposed addressing nonlinearity with fractional polynomials based on power transforms of predictors using real valued powers They proposed consideration of finite sets of powers. They recommended the eight powers −2, −1, −0.5, 0, 0.5, 1, 2, 3 (with the 0 case corresponding to the natural log transform) for degree 1 fractional polynomials based on a single power transform (for more details on standard fractional polynomial modeling see [2] [3]). Carroll and Ruppert [6] used these Box-Cox transforms to transform both outcomes and predictors
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
