Orthogonalization of regressors or comparison of log residual variances in reduced general linear models provides a simple solution to resolve multicollinearity between reward prediction error and reward outcomes in fMRI data.
Conventional neuroimaging techniques provide information about condition-related changes of the BOLD (blood-oxygen-level dependent) signal, indicating only where and when the underlying cognitive processes occur. Recently, with the help of a new approach called "model-based" functional neuroimaging (fMRI), researchers are able to visualize changes in the internal variables of a time varying learning process, such as the reward prediction error or the predicted reward value of a conditional stimulus. However, despite being extremely beneficial to the imaging community in understanding the neural correlates of decision variables, a model-based approach to brain imaging data is also methodologically challenging due to the multicollinearity problem in statistical analysis. There are multiple sources of multicollinearity in functional neuroimaging including investigations of closely related variables and/or experimental designs that do not account for this. The source of multicollinearity discussed in this paper occurs due to correlation between different subjective variables that are calculated very close in time. Here, we review methodological approaches to analyzing such data by discussing the special case of separating the reward prediction error signal from reward outcomes.
Erdeniz et al. (Tue,) conducted a review in fMRI methodology (multicollinearity in reward prediction error and reward outcomes). Orthogonalization of regressors in General Linear Models (GLM) vs. Non-orthogonalized regressors was evaluated on Model fit (explained unique BOLD variance and log residual variance). Orthogonalization of regressors or comparison of log residual variances in reduced general linear models provides a simple solution to resolve multicollinearity between reward prediction error and reward outcomes in fMRI data.