Fmri Glm Analysis Guide

fMRI GLM Analysis Guide

Purpose

The General Linear Model (GLM) is the standard statistical framework for task-based fMRI analysis. It models the observed BOLD time series as a linear combination of expected signal components (task regressors convolved with the hemodynamic response function) plus confound regressors plus noise (Poline & Brett, 2012; Poldrack et al., 2011, Ch. 4).

This skill encodes the domain-specific judgment needed to correctly specify a GLM for fMRI data. A competent programmer without neuroimaging training would get many of these decisions wrong -- choosing the wrong HRF model, setting an inappropriate high-pass filter cutoff, omitting critical confound regressors, or applying invalid statistical thresholds. Each decision described here requires understanding the biophysics of BOLD signal, the noise characteristics of fMRI data, and the statistical assumptions of the model.

When to Use This Skill

• Specifying a first-level (single-subject) GLM for task fMRI
• Choosing HRF models, confound regressors, and temporal filtering parameters
• Defining contrasts to test experimental hypotheses
• Setting up second-level (group) analyses
• Selecting appropriate multiple comparison correction methods
• Reviewing or troubleshooting an existing fMRI analysis pipeline

Research Planning Protocol

Before executing the domain-specific steps below, you MUST:

1. State the research question — What specific brain-behavior hypothesis is this GLM testing?
2. Justify the method choice — Why task fMRI with GLM? What alternatives (resting-state, EEG, behavior-only) were considered?
3. Declare expected outcomes — Which regions/contrasts do you expect to show effects, and in what direction?
4. Note assumptions and limitations — What does the GLM assume? Where could it mislead?
5. Present the plan to the user and WAIT for confirmation before proceeding.

For detailed methodology guidance, see the research-literacy skill.

⚠️ Verification Notice

This skill was generated by AI from academic literature. All parameters, thresholds, and citations require independent verification before use in research. If you find errors, please open an issue.

First-Level Analysis Decision Tree

Step 1: HRF Model Selection

The hemodynamic response function (HRF) models the neurovascular coupling delay between neural activity and the measured BOLD signal. The canonical HRF peaks at approximately 5-6 seconds post-stimulus (Glover, 1999).

Decision logic:

Is the HRF shape well-established for your task and population?
 |
 +-- YES --> Is timing precision critical to your hypothesis?
 | |
 | +-- YES --> Canonical + temporal derivative
 | |
 | +-- NO --> Canonical HRF (default)
 |
 +-- NO --> Do you have enough trials (>40 per condition) for stable estimation?
 |
 +-- YES --> FIR model (exploratory) or canonical + derivatives
 |
 +-- NO --> Canonical + temporal derivative (safest compromise)

Domain warning: When using derivative basis functions, the contrast for the main condition should weight only the canonical regressor (not the derivatives). An F-test across all basis functions tests whether any component differs from zero (Calhoun et al., 2004). See references/design-matrix-guide.md for details.

Step 2: High-Pass Filter Cutoff

Low-frequency drifts from scanner instability, subject physiology, and slow head motion must be removed. This is implemented as a discrete cosine transform (DCT) basis set added to the design matrix (Poldrack et al., 2011, Ch. 5).

• Default cutoff period: 128 seconds (0.0078 Hz) -- the SPM default, appropriate for most event-related and block designs (Poldrack et al., 2011, Ch. 5)
• Rule: The cutoff period must be at least 2x the longest interval between events of the same condition type (Poldrack et al., 2011, Ch. 5)
• Block designs: For a block design with 30-second blocks alternating between two conditions, the full cycle is 60 seconds. A 128-second cutoff safely preserves this signal
• Slow event-related designs: If trials of the same condition occur every 90 seconds, a 128-second cutoff is too aggressive. Use at least 180 seconds (2 x 90)

Domain warning: Setting the cutoff too low (long period) leaves drift in the data, inflating noise. Setting it too high (short period) attenuates your experimental signal. Always verify that your design's fundamental frequency is preserved by the filter.

Step 3: Confound Regression

Confound regressors model variance from non-neural sources. Omitting them inflates false positive rates; including too many reduces statistical power.

Motion Parameters

Head motion is the single largest source of structured artifact in fMRI (Power et al., 2012).

Domain insight: The 24-parameter model (Friston et al., 1996) captures both linear and nonlinear motion effects, including spin-history artifacts from previous-timepoint head positions. The squared terms model the nonlinear relationship between motion and BOLD signal changes.

Framewise Displacement and Spike Regressors

• Calculate framewise displacement (FD) as the sum of absolute values of the six motion derivatives, with rotations converted to mm on a 50-mm radius sphere (Power et al., 2012)
• Flag volumes with FD > 0.5 mm as motion spikes (Power et al., 2012); for more stringent control, use FD > 0.2 mm (Power et al., 2014)
• Model each spike as a separate indicator regressor (one column per flagged volume). This is mathematically equivalent to censoring/scrubbing but preserves the temporal structure of the design matrix

Physiological Noise: CompCor

When physiological recordings (pulse, respiration) are unavailable:

• aCompCor (anatomical CompCor): Extract top 5-6 principal components from white matter and CSF masks (Behzadi et al., 2007; Muschelli et al., 2014)
• tCompCor (temporal CompCor): Extract components from high-temporal-variance voxels (Behzadi et al., 2007)
• aCompCor is generally preferred because it uses anatomically defined noise ROIs and is less susceptible to removing neural signal (Ciric et al., 2017)

Domain warning -- global signal regression: Regressing out the global mean signal is controversial. It improves motion artifact removal but introduces artifactual anticorrelations in functional connectivity analyses (Murphy & Fox, 2017). For task-based GLM, global signal regression is generally not recommended unless specifically justified.

Step 4: Serial Autocorrelation Correction

fMRI time series exhibit temporal autocorrelation due to hemodynamic smoothing and physiological noise. Ignoring this inflates t-statistics and false positive rates (Woolrich et al., 2001).

Domain insight: Recent work has shown that AR(1) may be insufficient for modern multiband acquisitions with short TRs (< 1 s), where higher-order autocorrelation structure is present (Olszowy et al., 2019). For short-TR data, consider ARMA(1,1) or FSL's FILM approach.

Step 5: Construct and Verify the Design Matrix

Before fitting the model:

1. Visualize the design matrix -- Check for empty or near-empty columns, which indicate conditions with no events or events lost to the high-pass filter
2. Check condition-regressor correlation -- Correlation > 0.5 between task regressors indicates collinearity, reducing power and making contrasts uninterpretable (Mumford et al., 2015)
3. Verify the high-pass filter preserves signal -- Overlay the filter cutoff on the power spectrum of each task regressor
4. Inspect the variance inflation factor (VIF) -- VIF > 5 for any regressor indicates problematic multicollinearity (Poldrack et al., 2011, Ch. 4)

See references/design-matrix-guide.md for detailed guidance on design matrix construction.

Contrast Specification

Contrasts define the specific hypotheses you test within the fitted GLM.

t-Contrasts (Directional)

A t-contrast is a single row vector of weights applied to the parameter estimates. It tests a directional hypothesis.

Rules for valid t-contrasts (Poline & Brett, 2012):

• Weights must sum to zero for difference contrasts
• Only task regressors should receive non-zero weights (never confound regressors)
• When using derivative basis functions, contrast only the canonical regressor

F-Contrasts (Omnibus)

An F-contrast tests whether any of several effects are non-zero. It is specified as a matrix (multiple rows).

Domain insight: An F-test for the full basis set (canonical + derivatives) tests whether there is any evoked response, regardless of its exact timing or shape. This is more sensitive than a t-test on the canonical regressor alone when the true HRF deviates from canonical form (Calhoun et al., 2004).

Second-Level Analysis (Group Inference)

First-level contrast maps (one per subject) serve as input to the group model.

Fixed Effects vs. Mixed Effects

Decision logic:

Are you combining runs within one subject?
 |
 +-- YES --> Fixed effects (concatenation or run-by-run with FFX)
 |
 +-- NO --> Are you making group-level inferences?
 |
 +-- YES --> Mixed effects (FLAME in FSL) or OLS summary statistics
 OLS is valid and near-optimal for balanced designs
 (Mumford & Nichols, 2009)

Domain warning: Using a fixed-effects analysis for group inference treats between-subject variability as zero, dramatically inflating false positive rates. Results would apply only to the specific subjects scanned, not to the population (Friston et al., 2005; Mumford & Nichols, 2009).

Common Second-Level Designs

• One-sample t-test: Design matrix = intercept only (column of ones). Tests group mean activation against zero
• Two-sample t-test: Compares two groups (e.g., patients vs. controls). Include group-mean confounds (age, motion) as covariates
• Paired t-test: Within-subject comparison of two conditions at the group level
• ANOVA / Flexible factorial: Multiple factors; requires careful specification of variance components

Multiple Comparison Correction

With approximately 100,000 voxels tested simultaneously, correction for multiple comparisons is essential. See references/statistical-inference.md for detailed guidance.

Quick Reference

Critical domain knowledge: Cluster-based inference with a cluster-defining threshold (CDT) of p < 0.01 produces inflated false positive rates (up to 70% instead of the nominal 5%). Always use CDT of p < 0.001 or stricter (Eklund et al., 2016). For permutation tests, use at least 5,000-10,000 permutations for publication-quality results (Nichols & Holmes, 2002).