Sparse Single Index Mixed Model for Longitudinal Data

• Activity Number: 210
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Sijian Wang*+ and Peter Song and Ji Zhu
• Companies: University of Wisconsin-Madison and University of Michigan and University of Michigan
• Keywords: Longitudinal data ; Regularization ; Single index model ; Spline

Abstract

The single-index model is an important tool in multivariate nonparametric regression, which can avoid the so-called "curse of dimensionality" by searching a univariate index of the multivariate predictors to capture important features of high-dimensional data. Although it is widely applied to independent data, to our knowledge, the corresponding method to treat longitudinal data, which are commonly encountered in many biological and medical problems, is lacking in literature. In this talk, we consider a sparse single index mixed model for longitudinal data, which models the correlation among repeated measures by including random effects. By implementing certain regularization, our method can not only identify important fixed effects to construct the index, but also identify important random effects which are useful to model the correlation structure. We also proposed an effective method to fit the model. Numerical studies were considered to demonstrate our method.