Identifying FMRI model violations with Lagrange multiplier tests

Area of Science:

• Neuroimaging
• Cognitive Neuroscience
• Biomedical Engineering

Background:

• Standard functional magnetic resonance imaging (fMRI) models rely on linearity, time invariance, and stationarity assumptions.
• These assumptions are often unchecked due to a lack of accessible software, risking biased inferences in fMRI studies.
• Model violations are a significant but overlooked issue in fMRI data analysis.

Purpose of the Study:

• To develop simple, efficient procedures for detecting violations of standard fMRI model assumptions.
• To address the neglect of model checking in conventional fMRI analysis pipelines.
• To provide tools for identifying nonlinearity, nonstationarity, and hemodynamic response model (double gamma) validity issues.

Main Methods:

• Utilized Lagrange multiplier testing methods for developing detection procedures.
• Implemented computationally inexpensive tests easily integrated into existing fMRI analysis workflows.
• Calculated a test statistic per voxel, visualized as a spatial anomaly map indicating model violations.

Main Results:

• Developed and validated efficient procedures for detecting common fMRI model violations.
• Demonstrated the ability to identify nonlinearity, nonstationarity, and double gamma specification issues.
• Generated spatial anomaly maps highlighting regions with violated model assumptions in real fMRI data.

Conclusions:

• The developed Lagrange multiplier testing methods offer a computationally cheap and effective way to check fMRI model assumptions.
• These methods can be readily incorporated into standard fMRI analysis to enhance reliability and prevent mistaken inference.
• The spatial anomaly maps provide intuitive visualization of model violations, aiding researchers in data interpretation.