Consider the matrix formulation of the general linear model: $$\mathbf{Y} = \mathbf{M} \psi + \in$$ where \(Y\) is the vector of outcomes, \(M\) is the full design matrix (including nuisance covariates), \(\psi\) is the vector of parameter estimates, and \(\in\) is the vector of error terms. In a permutation framework, algorithms are applied differently depending on the presence/absence of nuisance covariates; thus the model is separated depending on the contrast of interest: $$\mathbf{Y} = \mathbf{X}\beta + \mathbf{Z}\gamma + \in$$ where \(\mathbf{X}\) contains covariates of interest, \(\mathbf{Z}\) contains nuisance covariates, and \(\beta\) and \(\gamma\) are the associated parameter estimates.
partition(M, con.mat, part.method = c("beckmann", "guttman"))Numeric matrix; the full design matrix
Numeric matrix; the contrast matrix
Character string; the method of partitioning (default:
beckmann)
A list containing:
Numeric matrix for the covariates of interest
Numeric matrix for the nuisance covariates
The effective contrast, equivalent to the original, for
the partitioned model [X, Z] and considering all covariates
Same as eCx, but considering only X
Guttman I. Linear Models: An Introduction. Wiley, New York, 1982.
Smith SM, Jenkinson M, Beckmann C, Miller K, Woolrich M (2007). Meaningful design and contrast estimability in fMRI. NeuroImage, 34(1):127-36.