Joint and Individual Component Regression.

Multi-group data, which include the same set of variables on separate groups of samples, 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. 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. We formulate this framework under the representation of latent components and propose an iterative algorithm to solve for the joint and individual scores. We utilize the Continuum Regression (CR) to estimate the latent scores, 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. We conduct simulation studies and analysis of an Alzheimer's disease dataset to further demonstrate the effectiveness of JICO. R package of JICO is available online at https://CRAN.R-project.org/package=JICO.