Risk Related Brain Regions Detection and Individual Risk Classification with 3D Image FPCA

Abstract

Understanding how people make decisions among risky choices has attracted much attention of researchers in economics, psychology, and neuroscience. While economists try to evaluate individual's risk preference through mathematical modeling, neuroscientists answer the question by exploring the neural activities in brain. We propose a novel model-free method, 3-dimensional image functional principal component analysis (3DIF), to provide a connection between active risk related brain region detection and individual's risk preference. The 3DIF methodology is directly applicable to 3D image data without artificial vectorization or mapping and simultaneously guarantees the contiguity of risk related brain regions rather than discrete voxels. Simulation study evidences an accurate and reasonable region detection using the 3DIF method. In real data analysis, 5 important risk related brain regions are detected, including parietal cortex (PC), ventrolateral prefrontal cortex (VLPFC), lateral orbifrontal cortex (lOFC), anterior insula (aINS) and dorsolateral prefrontal cortex (DLPFC), while the alternative methods only identify limited risk related regions. Moreover, the 3DIF method is useful for extraction of subjective specific signature scores that carry explanatory power for individual's risk attitude. In particular, the 3DIF method perfectly classifies both strongly and weakly risk averse subjects for in-sample analysis. In out-of-sample experiment, it achieves 73-88% overall accuracy, among which 90-100% strongly risk averse subjects and 49-71% for weakly risk averse subjects are correctly classified with leave-k-out cross validations. This is a joint work with Wolfgang Karl Haerdle, Qiang He and Piotr Majer.