title: Adaptive Modeling: An Approach for Incorporating Nonlinearity in Regression Analyses.
abstract: Although regression relationships commonly are treated as linear, this often is not the case. An adaptive approach is described for identifying nonlinear relationships based on power transforms of predictor (or independent) variables and for assessing whether or not relationships are distinctly nonlinear. It is also possible to model adaptively both means and variances of continuous outcome (or dependent) variables and to adaptively power transform positive-valued continuous outcomes, along with their predictors. Example analyses are provided of data from parents in a nursing study on emotional-health-related quality of life for childhood brain tumor survivors as a function of the effort to manage the survivors' condition. These analyses demonstrate that relationships, including moderation relationships, can be distinctly nonlinear, that conclusions about means can be affected by accounting for non-constant variances, and that outcome transformation along with predictor transformation can provide distinct improvements and can resolve skewness problems.© 2017 Wiley Periodicals, Inc.
authors.affiliation: School of Nursing, University of North Carolina at Chapel Hill, Room 5014 Carrington Hall Campus Box 7460 Chapel Hill, NC, 27599-7460.
authors.forename: George J
authors.initials: GJ
authors.lastname: Knafl
authors.affiliation: The Children's Hospital of Philadelphia, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA.
authors.forename: Lamia P
authors.initials: LP
authors.lastname: Barakat
authors.affiliation: School of Nursing, University of Pennsylvania, Philadelphia, PA.
authors.forename: Alexandra L
authors.initials: AL
authors.lastname: Hanlon
authors.affiliation: School of Nursing, University of Pennsylvania, Philadelphia, PA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Hardie
authors.affiliation: School of Nursing, University of North Carolina at Chapel Hill, Chapel Hill, NC.
authors.forename: Kathleen A
authors.initials: KA
authors.lastname: Knafl
authors.affiliation: The Children's Hospital of Philadelphia, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA.
authors.forename: Yimei
authors.initials: Y
authors.lastname: Li
authors.affiliation: School of Nursing, University of Pennsylvania, Philadelphia, PA.
authors.forename: Janet A
authors.initials: JA
authors.lastname: Deatrick
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D011788:Quality of Life; D012044:Regression Analysis; D011795:Surveys and Questionnaires; D017741:Survivors / Q000523:psychology*
keywords: adaptive regression; fractional polynomials; moderation; non-constant variance