Second-Level fMRI Data Analysis Using Mixed Model

Abstract

This chapter deals with the random effects in fMRI data analysis. To begin with, we give the background in using the mixed-effect model for second-level fMRI data processing. Because applying general linear mixed model (GLMM) method directly to second-level fMRI data analysis can lead to computational difficulties, we employ a method which projects the first-level variance for the second-level analysis, i.e., we adopt a two-stage mixed model to combine or compare different subjects. To estimate the variance for the mixed model analysis, we developed an expectation trust region algorithm. We provide detailed information about Newton–Raphson (NR) and (expectation) trust region algorithms for different run/subject combination and comparison. After the parameters have been estimated, the T statistic for significance inference was employed. Simulation studies using synthetic data were carried out to evaluate the accuracy of the methods for group combination and comparison. In addition, real fMRI dataset from retinotopic mapping experiment was employed to test the feasibility of the methods for second-level analysis. To improve the NR algorithm, we present Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm for the mixed model parameters estimation. We found that the method can improve the estimation for NR algorithm, but no significant improvement for trust region algorithms. Finally, we proposed an approach for degree of freedom (DF) estimation in the mixed-effect model. The idea is based on robust statistics. Using maximum-likelihood estimation method, we calculate the score function and Hessian matrices for the iteration expectation trust region algorithm for maximizing likelihood function. We then give NR and (expectation) trust region iteration algorithms for the DF estimation.