Modeling Functional Data with Spatially Heterogeneous Shape Characteristics
Article first published online: 3 NOV 2011
© 2011, The International Biometric Society
Volume 68, Issue 2, pages 331–343, June 2012
How to Cite
Staicu, A.-M., Crainiceanu, C. M., Reich, D. S. and Ruppert, D. (2012), Modeling Functional Data with Spatially Heterogeneous Shape Characteristics. Biometrics, 68: 331–343. doi: 10.1111/j.1541-0420.2011.01669.x
- Issue published online: 26 JUN 2012
- Article first published online: 3 NOV 2011
- Received November 2010. Revised July 2011., Accepted July 2011.
- Gaussian and t-copulas;
- Quantile modeling;
- Skewed functional data;
- Tractography data
Summary We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging (MRI).