The resultant second-order component find protocol is often denoted as “g.” This approach is particularly useful when tasks load heavily on multiple components, as it can simplify the task to first-order component weightings, making the factor solution more readily interpretable. A complication for this approach,

however, is that the underlying source of this second-order component is ambiguous. More specifically, while correlations between first-order components from the PCA may arise because the underlying factors are themselves correlated (for example, if the capacities of the MDwm and MDr networks were influenced by some diffuse factor like conductance speed or plasticity), they will also be correlated if there is “task mixing,” that is, if tasks tend to weigh on multiple independent factors. In behavioral factor analysis, these accounts are effectively indistinguishable as the components or latent variables cannot be measured directly. Here, we have an objective measure of the extent to which the tasks are mixed, as we know, based on the functional neuroimaging data, the extent to which the tasks recruit spatially separated functional networks

relative to rest. Consequently, it is possible to subdivide “g” into the proportion that is predicted by the mixing of tasks on multiple functional brain networks and the proportion LBH589 mw that may be explained

by other diffuse factors (Figure 3). Two simulated data sets mafosfamide were generated; one based on the loadings of the tasks on the MDwm and MDr functional networks (2F) and the other including task activation levels for the verbal network (3F). Each of the 44,600 simulated “individuals” was assigned a set of either two (2F) or three (3F) factor scores using a random Gaussian generator. Thus, the underlying factor scores represented normally distributed individual differences and were assumed to be completely independent in the simulations. The 12 task scores were assigned for each individual by multiplying the task-functional network loadings from the ICA of the neuroimaging data by the corresponding, randomly generated, factor score and summating the resultant values. The scores were then standardized for each task and noise was added by adding the product of randomly generated Gaussian noise, the test-retest reliabilities (Table S2), and a noise level constant. A series of iterative steps were then taken, in which the noise level constant was adjusted until the summed communalities from the simulated and behavioral PCA solutions were closely matched in order to ensure that the same total amount of variance was explained by the first-order components. This process was repeated 20 times to generate a standard deviation.