Searchlight-based multi-voxel pattern analysis of fMRI by   cross-validated MANOVA
  Multi-voxel pattern analysis (MVPA) is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data. We propose to replace the standard 'decoding' approach to searchlight-based MVPA, measuring the performance of a classifier by its accuracy, with a method based on the multivariate form of the general linear model. Following the well-established methodology of multivariate analysis of variance (MANOVA), we define a measure that directly characterizes the structure of multi-voxel data, the pattern distinctness $D$. Our measure is related to standard multivariate statistics, but we apply cross-validation to obtain an unbiased estimate of its population value, independent of the amount of data or its partitioning into 'training' and 'test' sets. The estimate $\hat D$ can therefore serve not only as a test statistic, but as an interpretable measure of multivariate effect size. The pattern distinctness generalizes the Mahalanobis distance to an arbitrary number of classes, but also the case where there are no classes of trials because the design is described by parametric regressors. It is defined for arbitrary estimable contrasts, including main effects (pattern differences) and interactions (pattern changes). In this way, our approach makes the full analytical power of complex factorial designs known from univariate fMRI analyses available to MVPA studies. Moreover, we show how the results of a factorial analysis can be used to obtain a measure of pattern stability, the equivalent of 'cross-decoding'. 
Carsten Allefeld, John-Dylan Haynes
q-bio.NC stat.AP