Table 2.

Derivation and validation in held-out data of the task-invariant CR activation pattern.

(1)	Randomly pick a derivation sample of 200 participants and assemble their task data in matrix array Y. Y has as many rows as voxels in the analysis, and 200*12 = 2400 columns.
(2)	Perform PCA on this data array; this yields an array of Principal Components in the matrix V; V has as many rows as voxels and 2399 columns since there are 2399 Principal Components. (The mean image, i.e. the mean across all columns, was removed from the data array Y prior to the PCA.)
(3)	Compute the PC scores W according to the formula: W = Y′ V. Here ‘ indicates matrix transposition. W has 2400 rows and 2399 columns.
(4)	Perform linear regressions where NARTIQ is predicted from the score array W. For every one of the N participants in the derivation sample NARTIQ is stacked 12 times, resulting in a dependent variable DV that has 200 × 12 = 2400 rows. The regression can be written as: DV = [W (:,1:k) 1] *β + ε, where the first k Principal Components are used for the array of independent variables, and 1 denotes an intercept term. The number k is determined with the best-fit AIC criterion. This concludes the model-estimation in the derivation sample.
(5)	A corresponding pattern can be constructed according to: pattern = V(:,1:k)*β(1:k). The pattern is normalized to have a Euclidean norm = 1.
(6)	Form the data array of the remaining 55 subjects in the replication sample, again subjects and tasks are stacked to form the data array Z which has as many rows as voxels and 55 × 12 = 660 columns.
(7)	Compute the PC scores in the replication sample with respect to the pattern derived in the derivation sample: w=Z′ pattern. The score vector w is a column vector with 660 rows. This score vector is the partial prediction of NART in the replication sample (minus an intercept term).It contains 12 predictions per participant. The predictions are averaged within subject.
(8)	The subject-wise prediction is then correlated with the actual NARTIQ values and the lodP statistic lodP = sign (R)* log10(p) is computed for tallying the quality of the prediction.
(9)	Steps 1–8 are executed 1000 times -each time a different random subset of participants is chosen- to yield 1000 activation patterns and 1000 lodP-values.
(10)	The 1000 patterns are averaged and re-normalized to compute a point estimate value of the task-invariant NARTIQ pattern.
(11)	The variability of the voxel-loadings of the 1000 patterns around the point estimate value is computed as a standard deviation. A coefficient-of-variation image is computed as: CV(i) = mean(i)/std(i), where i indicates the voxel location. CV is thresholded at ∣CV∣>3 to focus on inferentially robust voxels.