Spatial smoothing of autocorrelations to control the degrees of freedom in fMRI analysis

In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of temporal autocorrelations increases the effective df (but not the smoothness of primary or secondary parameter estimates), so that the amount of smoothing can be chosen in advance to achieve a target df, typically 100. This has already been done at the second level of a hierarchical analysis by smoothing the ratio of random to fixed effects variances (Worsley, K.J., Liao, C., Aston, J.A.D., Petre, V., Duncan, G.H., Morales, F., Evans, A.C., 2002. A general statistical analysis for fMRI data. NeuroImage, 15:1-15); we now show how to do it at the first level, by smoothing autocorrelation parameters. The proposed method is extremely fast and it does not require any image processing. It can be used in conjunction with other regularization methods (Gautama, T., Van Hulle, M.M., in press. Optimal spatial regularisation of autocorrelation estimates in fMRI analysis. NeuroImage.) to avoid unnecessary smoothing beyond 100 df. Our results on a typical 6-min, TR = 3, 1.5-T fMRI data set show that 8.5-mm smoothing is needed to achieve 100 df, and this results in roughly a doubling of detected activations.