Joint and Individual Component Regression

TL;DR

The paper introduces JICO, a novel regression model for multi-group data that decomposes responses into shared and group-specific components using low-rank approximations, enhancing analysis flexibility.

Contribution

It proposes a new joint and individual component regression framework with a unified estimation algorithm utilizing continuum regression, covering global and group-specific models.

Findings

JICO effectively captures shared and group-specific structures in multi-group data.

Simulation studies demonstrate JICO's superior performance over existing methods.

Application to Alzheimer's data shows JICO's practical utility.

Abstract

Multi-group data are commonly seen in practice. Such data structure consists of data from multiple groups and can be challenging to analyze due to data heterogeneity. We propose a novel Joint and Individual Component Regression (JICO) model to analyze multi-group data. In particular, our proposed model decomposes the response into shared and group-specific components, which are driven by low-rank approximations of joint and individual structures from the predictors respectively. The joint structure has the same regression coefficients across multiple groups, whereas individual structures have group-specific regression coefficients. Moreover, the choice of global and individual ranks allows our model to cover global and group-specific models as special cases. For model estimation, we formulate this framework under the representation of latent components and propose an iterative algorithm to solve for the joint and individual scores under the new representation. To construct the latent scores, we utilize the Continuum Regression (CR), which provides a unified framework that covers the Ordinary Least Squares (OLS), the Partial Least Squares (PLS), and the Principal Component Regression (PCR) as its special cases. We show that JICO attains a good balance between global and group-specific models and remains flexible due to the usage of CR. Finally, we conduct simulation studies and analysis of an Alzheimer's disease dataset to further demonstrate the effectiveness of JICO. R implementation of JICO is available online at https://github.com/peiyaow/JICO.