🧠 neuroscience

How to Improve the Reliability of Aperiodic Parameter Estimates in M/EEG: A Method Comparison

This study demonstrates that increasing the number of detected periodic peaks in the FOOOF toolbox reduces the reliability of broadband aperiodic parameter estimates in M/EEG data, and proposes a theory-driven "censored regression" method that removes expected periodic frequency ranges to produce more robust and reliable estimates.

Original authors: Kalamala, P., Clements, G. M., Gyurkovics, M., Chen, T., Low, K., Fabiani, M., Gratton, G.

Published 2026-02-21

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CC BY 4.0

Original authors: Kalamala, P., Clements, G. M., Gyurkovics, M., Chen, T., Low, K., Fabiani, M., Gratton, G.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine your brain's electrical activity (recorded via EEG or MEG) is like a busy city skyline at night.

From a distance, the skyline has a general shape: the lights get dimmer the higher up you look. This gradual dimming is the aperiodic activity (the "1/f" signal). Scientists are very interested in this shape because it tells us about the brain's overall health, age, and how much "effort" it's using.

However, right in the middle of that skyline, there are specific, bright skyscrapers (the periodic activity or brain waves like Alpha and Beta rhythms). These skyscrapers are real and important, but they mess up the measurement of the general dimming slope if you try to measure the whole skyline at once.

To get an accurate measurement of the "dimming slope," scientists use a tool called FOOOF. Think of FOOOF as a smart camera that tries to identify the skyscrapers, digitally remove them, and then measure the remaining skyline.

The Problem: The Camera is Too Flexible

The paper argues that the current version of this "camera" (FOOOF) is too flexible. It lets the user decide how many skyscrapers to look for.

If you tell it to look for 0 skyscrapers, it just measures the whole thing (including the buildings).
If you tell it to look for 1, it tries to find one big building and remove it.
If you tell it to look for 3, it hunts for three buildings.

The researchers found a major issue: The more skyscrapers you tell the camera to hunt for, the shakier and less reliable the final measurement becomes.

Why? Because the camera sometimes mistakes a random flicker of light (noise) for a skyscraper, or it misses a real one. Every time it guesses wrong about a building, it accidentally changes the shape of the remaining skyline. It's like trying to measure the slope of a hill while someone keeps randomly moving rocks on it. The more rocks you try to move, the less sure you are about the hill's true shape.

The Solution: The "Censored" Approach

Instead of letting the camera hunt for buildings dynamically, the authors propose a theory-driven "Censored Regression" method.

The Analogy:
Imagine you are a photographer trying to measure the slope of a hill, but you know for a fact that a specific row of trees (the Alpha waves) always blocks your view in the middle of the hill.

The Old Way (FOOOF): You try to identify exactly where each tree is in every single photo and cut them out. Sometimes you cut out a tree, sometimes you cut out a bush by mistake, and sometimes you miss a tree. Your final photos look different every time.
The New Way (Censored Regression): You simply say, "I know trees exist between 6 and 16 Hz. I will ignore that entire section of the photo for everyone." You don't try to find the trees; you just cut out that specific strip of the image for every single person and every single photo. Then, you measure the slope of the remaining parts (the bottom and the top).

What They Found

The researchers tested this on two groups of people: one sitting quietly (Resting State) and one doing a difficult mental task (Stop-Signal Task).

Reliability: The "Censored" method was much more consistent. If you took the same person's data and split it in half, the Censored method gave almost the same result both times. The "hunting for peaks" method gave different results every time.
Accuracy: The Censored method was better at detecting real changes. For example, it could clearly see that the brain's "slope" gets flatter as people get older, or gets steeper when a task gets harder. The other methods often missed these subtle changes because the "noise" from hunting for peaks drowned them out.
Fewer Mistakes: The old method sometimes produced "impossible" results (like a slope going up instead of down, which doesn't make sense for a brain). The new method almost never made this mistake.

The Takeaway

If you want to measure the "background hum" of the brain accurately:

Don't try to be too clever by letting software hunt for every single brain wave peak. It introduces too much error.
Do use a "Censored" approach: Based on what we already know about the brain, simply exclude the specific frequency range where we know the "skyscrapers" (brain waves) live, and measure the rest.

It's a simpler, more robust way to get a clear picture of the brain's true shape, making research on aging, attention, and mental health much more reliable.

1. Problem Statement

Recent years have seen a surge in interest regarding broadband aperiodic brain activity (the 1/f phenomenon) in M/EEG data, as it offers insights into neural excitation/inhibition balance, aging, and clinical conditions. However, accurately estimating aperiodic parameters (slope/exponent and offset/intercept) requires separating them from narrowband periodic oscillations (e.g., alpha, beta rhythms).

The dominant tool for this separation is the fooof (Fitting Oscillations & One-Over-F) toolbox (now specparam). While popular, fooof relies on a data-driven approach where the user sets a maximum number of peaks to detect. The authors hypothesize that this flexibility introduces variability:

Noise Sensitivity: Allowing the algorithm to detect a variable number of peaks (0, 1, 3, etc.) across trials or subjects may fit noise as if it were a peak, increasing estimation error.
Reliability Issues: This variability may reduce the internal consistency (reliability) of the resulting aperiodic parameters, thereby lowering statistical power in correlational and experimental studies.
Overfitting: High model fit (high $R^2$ ) achieved by adding more peaks may simply reflect fitting noise rather than true signal.

2. Methodology

The study compared various spectral estimation and parameterization methods across two distinct datasets:

Resting State Data: 52 adults (25–75 years) recorded with eyes open and eyes closed.
Stop-Signal Task Data: 34 young adults performing a multimodal stop-signal task (visual/auditory go and stop stimuli).

Analytic Pipeline Comparisons:
The authors systematically varied three factors:

Spectral Decomposition: Fast Fourier Transform (FFT) vs. Welch's method (Welch).
Aperiodic Estimation Methods:
- fooof variants: Allowing 0 peaks (fooof0), 1 peak (fooof1), or 3 peaks (fooof3).
- Full Regression: Linear regression on the entire log-log spectrum (ignoring peaks).
- Censored Regression (Proposed): A theory-driven approach where a fixed frequency range known to contain periodic activity (6–16 Hz, covering theta/alpha/beta) is excluded (censored) from the regression. The slope and intercept are calculated only on the remaining frequencies.
Data Aggregation: Single-trial estimates averaged vs. estimates derived from averaged spectra.

Evaluation Metrics:
The authors evaluated methods based on three criteria rather than just model fit ( $R^2$ ):

Outlier Frequency: The proportion of estimates yielding positive slopes (physiologically implausible for resting/task EEG, indicating noise or algorithmic failure).
Internal Consistency (Reliability): Odd-even split-half reliability (Spearman's $\rho$ ) of slope and intercept estimates.
Effect Size (Validity): The ability to detect known effects:
- Resting State: Correlation between age and slope; difference in slope between eyes-open vs. eyes-closed.
- Task: Difference in slope between high-demand vs. low-demand stop-signal conditions.

3. Key Contributions

Identification of a Reliability Trade-off: The study demonstrates that increasing the number of allowed peaks in fooof significantly decreases the internal consistency of aperiodic estimates and increases the number of trials required to achieve high reliability.
Proposal of Censored Regression: The authors introduce a theory-driven "censored regression" method. By pre-defining and excluding the frequency range where oscillations typically occur (6–16 Hz), the method ensures that every trial/subject is fitted on the exact same set of data points, eliminating trial-to-trial variability in peak detection.
Empirical Validation: The paper provides a comprehensive benchmark showing that censored regression outperforms standard fooof settings (especially fooof1 and fooof3) in reliability and effect size detection, while avoiding the overfitting issues of data-driven peak detection.

4. Key Results

A. Outliers (Positive Slopes)

Methods allowing peak detection (fooof1, fooof3) generated a significantly higher percentage of positive slope estimates (indicating power increasing with frequency) compared to regression-only methods.
These positive slopes were often artifacts of the fitting procedure rather than genuine physiological signals, particularly when using FFT-based spectra.

B. Reliability (Internal Consistency)

Peak Count Impact: Reliability (odd-even correlation) decreased as the number of allowed peaks increased.
- fooof0 and Full Regression showed the highest reliability ( $\rho > 0.9$ ).
- Censored Regression also achieved high reliability ( $\rho > 0.9$ ).
- fooof1 and fooof3 showed significantly lower reliability ( $\rho < 0.86$ ).
Trials Required: To reach 90% reliability, fooof models with peaks required substantially more trials (sometimes >100) compared to regression methods (30–40 trials).
Spectral Method: In task-based data, combining FFT with multi-peak fooof models resulted in the lowest reliability. Welch's method generally performed better but did not fully mitigate the peak-count issue.

C. Effect Size (Statistical Power)

Age Effect: fooof3 showed the highest correlation with age, but the authors argue this may be confounded by residual alpha activity (as fooof sometimes fails to detect alpha in all subjects). Censored regression provided robust, large effect sizes without this confound.
Task Demand Effect: In the stop-signal task, Censored Regression yielded the largest effect sizes for the difference between high and low demand conditions.
- Surprisingly, fooof0 and Full Regression (which ignore peaks entirely) produced smaller effect sizes than Censored Regression. This suggests that while ignoring peaks is reliable, it is less valid for detecting specific aperiodic changes because the unremoved periodic activity biases the slope.
- Conclusion: Censored Regression offers the optimal balance: it removes the confounding periodic activity (unlike Full Regression) while maintaining fixed fitting parameters (unlike fooof).

5. Significance and Recommendations

Psychometric Validity: The study establishes that internal consistency is a prerequisite for valid correlational research. Data-driven peak fitting in fooof introduces unnecessary variance that deflates correlations.
Best Practice: The authors recommend Censored Regression as the preferred method for estimating aperiodic parameters in M/EEG.
- Procedure: Exclude the 6–16 Hz range (or a study-specific range based on prior literature) from the spectrum, then perform linear regression on the remaining log-log data.
- Advantage: This approach guarantees that the same number of data points are used for every estimate, maximizing reliability and statistical power while effectively controlling for periodic oscillations (like alpha) that would otherwise bias the slope.
Limitations: The method does not provide estimates of the periodic peaks themselves (frequency, power, bandwidth). The authors suggest a two-step approach: use censored regression for the aperiodic component, subtract it, and then analyze the residual for periodic features.
Generalizability: While the specific 6–16 Hz range is based on scalp EEG, the core principle—that fixed, theory-driven exclusion of periodic ranges improves reliability over variable, data-driven peak detection—applies broadly to M/EEG analysis.

In summary, the paper argues that the pursuit of "perfect" model fit via data-driven peak detection in fooof comes at the cost of reliability and validity. A simpler, theory-driven exclusion of known oscillatory bands (Censored Regression) yields more robust, reliable, and powerful estimates of the 1/f aperiodic signal.