Orthogonalization of Regressors in fMRI Models (original) (raw)
Fig 2
Illustration of parameter estimate behavior for 20 simulated subjects when model has low collinearity (top), high collinearity (middle) and high collinearity where the feedback regressor is orthogonalized with respect to the stimulus regressor (bottom).
The Venn diagrams indicate how the variability is distributed across the 2 regressors where red is unique to stimulus, blue is unique to feedback and purple is shared. The rightmost column shows the parameter estimates for stimulus (red) and feedback (blue) across 20 subjects, where the solid lines indicate the true values. With low collinearity the variability of the parameter estimates is much smaller than the high collinearity case, although in both cases the estimates are unbiased on average. Orthogonalization does not change the feedback parameter estimates (middle and bottom blue data points are identical), but the stimulus feedback has lower variability and the estimate is much higher.