Bayesian Quantile Latent Factor on Image Regression

Abstract

This paper considers a quantile latent factor-on-image (Q-LoI) regression model to comprehensively investigate the relationship between the latent factor of interest and scalar and imaging predictors at different quantiles. The latent factor is characterized by several manifest variables through a confirmatory factor analysis model and then regressed on scalar and imaging covariates. We propose a two-stage method to conduct statistical inference. The first stage extracts leading features from the imaging data through the functional principal component analysis (FPCA) method. The second stage incorporates the extracted imaging features into the Q-LoI regression to examine the impacts of scalar and imaging covariates on the latent factor under various quantiles. A fully Bayesian method with Markov Chain Monte Carlo (MCMC) algorithms is developed for parameter estimation. Simulation studies demonstrate the satisfactory performance of the proposed method. An application to the Alzheimer’s disease study is presented to confirm the utility of our methodology.

Keywords:

• Bayesian approach
• FPCA
• imaging data
• latent factor
• quantile regression

Additional information

Funding

This research was fully supported by GRF grant 14301918 from the Research Grant Council of the Hong Kong Special Administrative Region.