Applications of Hierarchical Modeling in Neuroimaging

The traditional group analysis approaches typically include simple methods such as Student's t-tests, ANOVA, and GLM, and nonparametric methods such as permutation testing handle similar data structures. Due to the complexities involved in neuroimaging data, more modeling capabilities are desirable under some circumstances. Here we discuss a flexible modeling platform, hierarchical (sometimes referred to as multilevel or mixed-effects) modeling, that not only contain the conventional approaches as special cases, but also open the door for more adaptable scenarios. Four modeling extensions will be covered under the hierarchical modeling framework: 1) including measurement error for the effect estimate in the analysis (and abandoning the homoscedastic assumption in the conventional approaches) as implemented in 3dMEMA, 2) handling thorny situations such as missing data, within-subject covariates, and trend analysis with 3dLME, 3) inter-subject correlation analysis for naturalistic scanning (3dISC), and 4) reliability measure of intraclass correlation (3dICC).