Using conditional maximization to determine hyperparameters in model-based fMRI

In model-based analysis of fMRI data, a neural or cognitive mathematical model of behavior is used to predict changes in fMRI activity. The model predictions are often applied as a parametric modulation of the main stimulus effect within the context of the general linear model (GLM). Using a mathematical model has become an important method for connecting fMRI signals to behavior because the model represents how stimulus processing leads to behavior, and the parametric modulation represents a specific test about the profile of stimulus-related fMRI activity (for review and discussion, see O'Doherty et al., 2007). However, in some cases the parameters of the mathematical model may be under-determined because there is a range of values that equally well account for behavior, or perhaps an exploratory analysis is desired. Thus, in order to fully gauge the applicability of some mathematical model it would be useful to understand how fMRI analysis depends on those parameters. Here, a conditional maximization procedure is developed to search for parameter values in the mathematical model as hyperparameters in the GLM. Simulations and analysis with real fMRI data show that conditional maximization is an effective and simple procedure for estimating hyperparameters. General recommendations and caveats for using hyperparameters in model-based fMRI analysis are also presented.