Fig. 8.

Optimising the basis set for the GLM analysis.

We used real data from a change-of-plan experiment (see the main text) to compare different basis sets for the GLM analysis. The different curves represent different frequencies: 5 Hz (blue), 7 Hz (red), 10 Hz (green) and 12 Hz (cyan)—as the results can vary depending on empirical responses.

A. Optimising the number of basis functions in the Fourier set using F-test. The black curve shows the threshold of significance at p = 0.05. Note that the threshold increases when adding regressors (basis function components) to the design matrix, due to the implicit change in the degrees of freedom. The optimal number here is the highest number above the threshold line (between 9 and 13 Hz depending on frequency).

B. Comparing non-nested basis sets, Fourier (solid lines) and Fourier Hanning (dotted lines) using Parametric Empirical Bayes. Here the optimal basis set is the one with the peak model evidence (approximated by free energy). For each frequency we subtracted the minimal free energy value from the other values. For all frequencies except 5 Hz the Fourier basis set had higher evidence and the optimal number of basis functions was between 8 and 13 consistent with the F-test results.