Electronic Journal of Statistics

Cluster analysis of longitudinal profiles with subgroups

Xiaolu Zhu and Annie Qu

Full-text: Open access

Abstract

In this paper, we cluster profiles of longitudinal data using a penalized regression method. Specifically, we allow heterogeneous variation of longitudinal patterns for each subject, and utilize a pairwise-grouping penalization on coefficients of the nonparametric B-spline models to form subgroups. Consequently, we identify clusters based on different patterns of the predicted longitudinal curves. One advantage of the proposed method is that there is no need to pre-specify the number of clusters; instead the number of clusters is selected automatically through a model selection criterion. Our method is also applicable for unbalanced data where different subjects could have measurements at different time points. To implement the proposed method, we develop an alternating direction method of multipliers (ADMM) algorithm which has the desirable convergence property. In theory, we establish the consistency properties for approximated nonparametric function estimation and subgrouping memberships. In addition, we show that our method outperforms the existing competitive approaches in our simulation studies and real data example.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 171-193.

Dates
Received: August 2016
First available in Project Euclid: 31 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1517367715

Digital Object Identifier
doi:10.1214/17-EJS1389

Mathematical Reviews number (MathSciNet)
MR3756096

Zentralblatt MATH identifier
06841002

Keywords
ADMM longitudinal data minimax concave penalty model selection nonparametric spline method

Rights
Creative Commons Attribution 4.0 International License.

Citation

Zhu, Xiaolu; Qu, Annie. Cluster analysis of longitudinal profiles with subgroups. Electron. J. Statist. 12 (2018), no. 1, 171--193. doi:10.1214/17-EJS1389. https://projecteuclid.org/euclid.ejs/1517367715


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