Combining Functional MRI Data on Multiple Subjects

Worsley et al. (2002) propose a practical approach to multiple-subject functional MRI data analyses which uses the EM algorithm to estimate the between-subject variance component at each voxel. The main result of this article is a demonstration that the much more efficient Newton-Raphson algorithm can be reliably used for these calculations. This result follows from an extension of a simple algorithm proposed by Mandel and Paule (1970) for the one-way unbalanced ANOVA model, two variants of which have been shown to be equivalent to modified ML and REML, in which the “modification” is that the within-subject variances as treated as known.