Sparse Single Index Models for Multivariate Responses

ABSTRACT

Joint models are popular for analyzing data with multivariate responses. We propose a sparse multivariate single index model, where responses and predictors are linked by unspecified smooth functions and multiple matrix level penalties are employed to select predictors and induce low-rank structures across responses. An alternating direction method of multipliers based algorithm is proposed for model estimation. We demonstrate the effectiveness of proposed model in simulation studies and an application to a genetic association study. Supplementary materials for this article are available online.

KEYWORDS:

• Alternating direction method of multipliers
• High dimension
• Multivariate response
• Single index model
• Sparsity

Supplementary Materials

Additional derivations: The supplementary materials contain a derivation of the gradient formulas used in updating the B matrix (see Section 3.2).

Plots: The supplementary materials contain illustration plots of the link functions used for simulation in Section 5 and the 62 estimated responses from the genetic association study in Section 6.

Tables: The supplementary materials contain tables comparing different methods in Section 5.

Code: The supplementary materials contain R code implementing the methods in this article.

Acknowledgments

All plots were made using the R (R Core Team 2013) and the R package ggplot2 (Wickham 2009).

Additional information

Funding

This research was funded in part by the National Institutes of Health (NIH) National Institute of Neurological Disorders and Stroke (NINDS) (R01NS091307 to L.X.) and in part by the National Institute on Aging (NIA) (R56AG064803 to L.X.). This work represents the opinions of the researchers and not necessarily that of the granting organizations.