AUTHOR=Ryoo Ji Hoon , Long Jeffrey D. , Welch Greg W. , Reynolds Arthur , Swearer Susan M. 

TITLE=Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data

JOURNAL=Frontiers in Psychology

VOLUME=8

YEAR=2017

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.01431

DOI=10.3389/fpsyg.2017.01431

ISSN=1664-1078

ABSTRACT=<p>As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM) that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.</p>