Generalized likelihood ratio tests for complex fMRI data: a simulation study

Statistical tests developed for the analysis of (intrinsically complex valued) functional magnetic resonance time series, are generally applied to the data's magnitude components. However, during the past five years, new tests were developed that incorporate the complex nature of fMRI data. In particular, a generalized likelihood ratio test (GLRT) was proposed based on a constant phase model. In this work, we evaluate the sensitivity of GLRTs for complex data to small misspecifications of the phase model by means of simulation experiments. It is argued that, in practical situations, GLRTs based on magnitude data are likely to perform better compared to GLRTs based on complex data in terms of detection rate and constant false alarm rate properties.