Risk related brain regions detection and individual risk classification with 3D image FPCA

Understanding how people make decisions from risky choices has attracted increasing 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 of the brain. We propose a 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 3-dimensional 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, five 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 weakly risk averse subjects are correctly classified with leave-k-out cross validations.