Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data - Ryoo, Ji Hoon; Long, Jeffrey D.; Welch, Greg W.; Reynolds, Arthur; Swearer, Susan M. (Frontiers in Psychology, 2017)
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 that can be applied to model nonlinear 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 fractional polynomial model for such applications.