  Representational similarity analysis (RSA) is a multivariate technique to
investigate cortical representations of objects or constructs. While avoiding
ill-posed matrix inversions that plague multivariate approaches in the presence
of many outcome variables, it suffers from the confound arising from the
non-orthogonality of the design matrix. Here, a partial correlation approach
will be explored to adjust for this source of bias by partialling out this
confound in the context of the searchlight method for functional imaging
datasets. A formal analysis will show the existence of a dependency of this
confound on the temporal correlation model of the sequential observations,
motivating a data-driven approach that avoids the problem of misspecification
of this model. However, where the autocorrelation locally diverges from its
volume estimate, bias may be difficult to control for exactly, given the
difficulties of estimating the precise form of the confound at each voxel.
Application to real data shows the effectiveness of the partial correlation
approach, suggesting the impact of local bias to be minor. However, where the
control for bias locally fails, possible spurious associations with the
similarity matrix of the stimuli may emerge. This limitation may be intrinsic
to RSA applied to non-orthogonal designs. The software implementing the
approach is made publicly available
(https://github.com/roberto-viviani/rsa-rsm.git).
