Abstract
Model-based analysis of fMRI data is an important tool for investigating the computational role of different brain regions. With this method, theoretical models of behavior can be leveraged to find the brain structures underlying variables from specific algorithms, such as prediction errors in reinforcement learning. One potential weakness with this approach is that models often have free parameters and thus the results of the analysis may depend on how these free parameters are set. In this work we asked whether this hypothetical weakness is a problem in practice. We first developed general closed-form expressions for the relationship between results of fMRI analyses using different regressors, e.g., one corresponding to the true process underlying the measured data and one a model-derived approximation of the true generative regressor. Then, as a specific test case, we examined the sensitivity of model-based fMRI to the learning rate parameter in reinforcement learning, both in theory and in two previously-published datasets. We found that even gross errors in the learning rate lead to only minute changes in the neural results. Our findings thus suggest that precise model fitting is not always necessary for model-based fMRI. They also highlight the difficulty in using fMRI data for arbitrating between different models or model parameters. While these specific results pertain only to the effect of learning rate in simple reinforcement learning models, we provide a template for testing for effects of different parameters in other models.
Highlights
The advent of fMRI revolutionized psychology as it allowed, for the first time, the noninvasive mapping of human cognition
Because we were primarily interested in the value signal, we focused on data from an regions of interest (ROIs) in the ventromedial prefrontal cortex
We showed that regression coefficients when using a model-based regressor, and their corresponding Student t values, depend on three factors: the contrast-to-noise ratio (CNR) in the signal, the number of data points in the regression, and ρ(xg, xf)—the correlation between the regressor generated with the fit parameter values, xf, and a regressor generated with the ground truth parameter values, xg
Summary
The advent of fMRI revolutionized psychology as it allowed, for the first time, the noninvasive mapping of human cognition. Model-based fMRI methods have been developed to overcome this limitation by using computational models of behavior to shed light on latent variables of the models (such as prediction errors) and their mapping to neural structures. This approach has led to important insights into the algorithms employed by the brain and has been successful in understanding the neural basis of reinforcement learning In a typical model-based fMRI analysis, one first specifies a model that describes the hypothesized cognitive processes underlying the behavior in question These models have one or more free parameters (e.g. learning rate in a model of trial-and-error learning). The fully specified model is used to generate trial-by-trial measures of latent variables in the model (e.g. action values and prediction errors) that can be regressed against neural data in order to find areas whose activity correlates with these variables in the brain
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