## Residual Analysis for Detecting Mis-modeling in fMRI.

Citation: Loh, J. M., Lindquist, M. A., Wager, T. D. (2008). Residual Analysis for Detecting Mis-modeling in fMRI. Statistica Sinica, 18, 1421-1448.

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### Abstract:

The voxel-wise general linear model (GLM) approach has arguably become the dominant way to analyze

functional magnetic resonance imaging (fMRI) data. The approach relies on specifying predicted patterns of

signal change a priori. In this work we develop methods for detecting mis-modeling in the GLM framework,

and derive mathematical expressions for quantifying the e?ects this has on bias and power. We show that

even a relatively small amount of mis-modeling can result in severe power loss, and can in?ate the false

positive rate beyond the nominal value. Due to the massive amount of data, examining the appropriateness

of the model is challenging in fMRI. We propose a simple procedure involving the residuals that can be used

to identify possible voxels or regions of the brain where model mis?t may be present. The key idea is that

if there is model mis?t ? such as a mis-speci?cation of onset, duration, or response shape ? residuals will

be systematically larger in mis-modeled segments of the time series. By looking at the weighted sum of

consecutive residuals using a moving window, our method can pick out regions of a residual time series in

which the residuals are consistently larger than expected by chance, while ignoring spurious large residuals

that are expected based on the noise distribution. It may also be used more generally for identifying arti-

facts in fMRI time courses. We investigate the e?ectiveness of this method using a simulation study, and by

applying it to an fMRI dataset. We develop a method and accompanying software for creating whole-brain

maps showing power loss and bias due to mis-modeling. Such maps could be a valuable tool in assessing

violations of statistical assumptions and informing about di?erences in the shape and timing of the hemo-

dynamic response function (HRF) across the brain.

Key words: fMRI, GLM, model diagnosis, model mis?t, power, residual analysis