Bayesian Nonparametric Longitudinal Data Analysis
成果类型：
Article
署名作者：
Quintana, Fernando A.; Johnson, Wesley O.; Waetjen, L. Elaine; Gold, Ellen B.
署名单位：
Pontificia Universidad Catolica de Chile; University of California System; University of California Irvine; University of California System; University of California Davis; University of California System; University of California Davis
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2015.1076725
发表日期：
2016
页码：
1168-1181
关键词：
linear mixed models
COVARIANCE-MATRIX
mixture
distributions
population
inference
priors
摘要：
Practical 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.