Robust and unbiased variance of GLM coefficients for misspecified autocorrelation and hemodynamic response models in fMRI

As a consequence of misspecification of the hemodynamic response and noise variance models, tests on general linear model coefficients are not valid. Robust estimation of the variance of the general linear model (GLM) coefficients in fMRI time series is therefore essential. In this paper an alternative method to estimate the variance of the GLM coefficients accurately is suggested and compared to other methods. The alternative, referred to as the sandwich, is based primarily on the fact that the time series are obtained from multiple exchangeable stimulus presentations. The analytic results show that the sandwich is unbiased. Using this result, it is possible to obtain an exact statistic which keeps the 5% false positive rate. Extensive Monte Carlo simulations show that the sandwich is robust against misspeci cation of the autocorrelations and of the hemodynamic response model. The sandwich is seen to be in many circumstances robust, computationally efficient, and flexible with respect to correlation structures across the brain. In contrast, the smoothing approach can be robust to a certain extent but only with specific knowledge of the circumstances for the smoothing parameter.