A multivariate regression framework for the analysis of fMRI data accounting for spatial correlation

Local canonical correlation analysis (CCA) is a multivariate method that simultaneously analyzes the timecourses of a group of neighboring voxels and has been demonstrated to be more sensitive than the conventional univariate GLM approach. However, unlike the general linear model (GLM), an arbitrary linear contrast of the temporal regressors has not been so far incorporated in the CCA formalism. To address the first problem, a multivariate regression model is presented which is a direct extension of univariate GLM. Mathematically, multivariate regression model is equivalent to CCA, but easier to interpret since the framework is similar to GLM. Arbitrary contrasts can be used in the multivariate regression model (MRM) approach including multivariate contrasts. With multivariate contrasts, it is also possible to test for significance of contrasts on regression coefficients as well as contrasts on voxels. The test for contrasts on voxels is not possible in the univariate framework. Furthermore, a constrained version of MRM is introduced which not only has more sensitivity than univariate GLM, but also corrects for the potential loss of specificity due to over-fitting in the multivariate model.