fMRI model diagnostics for the Double Gamma and temporal derivative

Standard analysis techniques for Functional Magnetic Resonance Imaging (fMRI) assume a linear, time invariant model of underlying signal behaviour. These assumptions are valid for some but not all data. Hence each model characteristic should be formally tested for its validity when analysing particular data. Diagnosing model violations is a necessary step in statistical modeling but is not yet common in fMRI. In general this would be a computationally demanding task. We present a test for the validity of the hemodynamic model comprising a Double Gamma function and its temporal derivative. Using the so-called Lagrange Multiplier method, the test only requires fitting under the statistical null hypothesis leading to simple implementation and fast computation. The method is demonstrated with simulated and real data examples.