The estimation of an optimal regularization parameter from empirical data has an unfortunate byproduct: putative measures of interest, including different ERP components, EEG spectra or time-frequency measures, will be associated with different optimal λ values. This concern also applies to different experimental conditions, study groups, or individual subjects. Because it is rather undesirable to modify the spline computation algorithm within a given study or analysis, as a rule-of-thumb, previous ‘optimal’ λ values provide an appropriate choice, and eliminate the possibility of an arbitrary regularization parameter selection (cf. Nunez and Srinivasan, 2006). We have repeatedly found that a λ value of 10−5 serves as a robust regularization constant for a wide range of EEG/ERP applications for a commonly-used spherical spline order (m = 4), yielding surprisingly similar CV minima when compared with the CV optimum (e.g., for the N1 sink topographies shown in Fig. 9 with m = 4, optimal and default values of λ corresponded to CV criterion values of 9.4952 and 9.5264, respectively).
