Risk related brain regions detected with 3D image FPCA

Risk attitude and perception is reflected in brain reactions during RPID experiments. Given the fMRI data, an important research question is how to detect risk related regions and to investigate the relation between risk preferences and brain activity. Conventional methods are often insensitive to or misrepresent the original spatial patterns and interdependence of the fMRI data. In order to cope with this fact we propose a 3D Image Functional Principal Component Analysis (3D Image FPCA) method that directly converts the brain signals to fundamental spatial common factors and subject-specific temporal factor loadings via proper orthogonal decomposition. Simulation study and real data analysis show that the 3D Image FPCA method improves the quality of spatial representations and guarantees the contiguity of risk related regions. The selected regions provide signature scores and carry explanatory power for subjects' risk attitudes. For in-sample analysis, the 3D Image method perfectly classifies both strongly and weakly risk averse subjects. In out-of-sample, it achieves 73-88% overall accuracy, with 90-100% rate for strongly risk averse subjects, and 49-71% for weakly risk averse subjects.