Department of Educational Psychology


Date of this Version



Ryoo JH, Long JD, Welch GW, Reynolds A and Swearer SM (2017) Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data. Front. Psychol. 8:1431. doi: 10.3389/fpsyg.2017.01431


Copyright © 2017 Ryoo, Long, Welch, Reynolds and Swearer. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY).


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.