Bayesian Nonparametric Longitudinal Data Analysis
Fernando Andrés Quintana, Wesley O. Johnson, L. Elaine Waetjen, Ellen B. Gold · Journal of the American Statistical Association · 2015
Fernando A. Quintanaa*, Wesley O. Johnsonb, L. Elaine Waetjenc & Ellen B. Goldca Departamento de Estadística, Pontificia Universidad Católica de Chile Santiago, Chileb Department of Statistics, University of California Irvine, Irvine, CA, USAc Department of Obstetrics and Gynecology, and Department of Public Health Sciences, Division of Epidemiology, University of California Davis, Davis, CA, USACONTACT Fernando A. Quintana [email protected] Departamento de Estadística, Pontificia Universidad Católica de Chile Santiago, ChileABSTRACTPractical Bayesian nonparametric methods have been developed across a wide variety of contexts. Here, we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry (CS) and autoregressive (AR) covariance structures. AR structure is often specified through the use of a Gaussian process (GP) with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart. We allow for AR structure by considering a broader class of models that incorporates a Dirichlet process mixture (DPM) over the covariance parameters of the GP. We are able to take advantage of modern Bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations. We also take advantage of the generality of our model, which provides for estimation of a variety of covariance structures. We observe that models that fail to incorporate CS or AR structure can result in very poor estimation of a covariance or correlation matrix. In our illustration using hormone data observed on women through the menopausal transition, biology dictates the use of a generalized family of sigmoid functions as a model for time trends across subpopulation categories.