Statistical Analysis of fMRI Time-Series: A Critical Review of the GLM Approach

Abstract

Functional magnetic resonance imaging (fMRI) is one of the most widely used tools to study the neural underpinnings of human cognition. Standard analysis of fMRI data relies on a general linear model (GLM) approach to separate stimulus induced signals from noise. Crucially, this approach relies on a number of assumptions about the data which, for inferences to be valid, must be met. The current paper reviews the GLM approach to analysis of fMRI time-series, focusing in particular on the degree to which such data abides by the assumptions of the GLM framework, and on the methods that have been developed to correct for any violation of those assumptions. Rather than biasing estimates of effect size, the major consequence of non-conformity to the assumptions is to introduce bias into estimates of the variance, thus affecting test statistics, power, and false positive rates. Furthermore, this bias can have pervasive effects on both individual subject and group-level statistics, potentially yielding qualitatively different results across replications, especially after the thresholding procedures commonly used for inference-making.

Keywords: autocorrelation; blood oxygenation level-dependent; fixed effects; functional magnetic resonance imaging; general linear model; mixed effects; multicollinearity; ordinary least squares.

Figure 1

Depiction of the GLM model for an imaginary voxel with time-series Y predicted by a design matrix X including 10 effects (three regressors of interest – e. g., tasks A,B,C – and seven nuisance regressors – e.g., six motion parameters and one linear drift) of unknown amplitude β_i, and an error term.