TITLE:
Adaptive Fractional Polynomial Modeling
AUTHORS:
George J. Knafl
KEYWORDS:
Adaptive Regression, Childhood Chronic Conditions, Fractional Polynomials, Moderation, Nonlinearity
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.1,
February
26,
2018
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.