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Beyond the mean: Sequence analysis methods for clustering ordinal EMA data

This paper proposes a method for clustering longitudinal ecological momentary assessment (EMA) data by applying sequence analysis measures followed by PCA and $K$ -means clustering, demonstrating that this approach better captures dynamic temporal patterns and improves the characterization of individual profiles compared to traditional latent class or transition analyses.

Original authors: Tianyi Wang, Anna L. Smith, Jillian R. Silva-Jones, Wendy Berry Mendes, Lauren N. Whitehurst

Published 2026-04-28

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CC BY 4.0

Original authors: Tianyi Wang, Anna L. Smith, Jillian R. Silva-Jones, Wendy Berry Mendes, Lauren N. Whitehurst

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The "Mood Playlist" Problem: A Simple Guide to New Ways of Understanding Stress

Imagine you are trying to understand your friend’s personality. You have two ways to do it:

The "Average" Method: You ask them, "On a scale of 1 to 10, how stressed are you?" every day for a month. At the end, you take the average. If they say "5" every single day, their average is 5.
The "Playlist" Method: You look at the rhythm of their month. One friend might be a "Steady 5"—calm, consistent, and predictable. Another friend might be a "Rollercoaster"—totally chill on Monday, a screaming panic on Tuesday, calm on Wednesday, and a meltdown on Thursday.

Even though both friends have an average stress level of 5, they are completely different people. The first is a calm lake; the second is a stormy ocean.

Most scientists currently use the "Average" Method. They take all that detailed, moment-by-moment data (called EMA data) and squash it down into one single number. The problem? They lose the "rhythm"—the patterns, the sudden jumps, and the stability that actually tell us how a person is doing.

What this paper does: Finding the "Rhythm" of Stress

The researchers in this paper wanted to stop "squashing" the data. They wanted to find groups of people who share the same stress rhythm.

To do this, they borrowed a trick from biologists who study DNA. DNA is just a long sequence of letters (A, C, G, T). Instead of looking at the "average letter" in a strand of DNA, biologists look at the patterns (like "how often does an A follow a G?").

The researchers applied this to stress. They looked at:

The Volume: How loud (intense) is the stress?
The Tempo: How fast is the stress changing from one moment to the next?
The Stability: Is the person staying in one mood, or are they constantly switching gears?

The "Sorting Hat" (The Method)

Once they had these "rhythms," they used a mathematical "Sorting Hat" (a combination of PCA and K-means clustering) to group people.

Think of it like sorting a massive pile of laundry. Instead of just sorting by "color" (the average), they sorted by "texture, weight, and frequency of use." This allowed them to find three distinct "Stress Tribes":

The Zen Masters (Cluster 1): Low stress, very stable. They are the "calm lakes."
The Storm Chasers (Cluster 2): High stress, high volatility. They are the "rollercoasters" who jump between moods constantly.
The Low-Key Drifters (Cluster 3): Generally low stress, but with a bit more "wobble" than the Zen Masters.

Why does this matter? (The Memory Test)

The researchers didn't just want to group people for fun; they wanted to see if these "rhythms" actually affect our brains. They looked at how these stress groups performed on memory tests.

They found that if you only look at the average stress, you miss part of the story. By using these "rhythm groups," they could better predict how well someone’s memory would work. It turns out, how your stress moves through your life is just as important as how much stress you have.

The Big Picture

In short: This paper is moving science away from "How much do you feel?" toward "How do you feel over time?"

By treating our emotions like a musical composition rather than a single note, we can get a much clearer picture of our mental health and how it impacts our ability to think, learn, and remember.

Technical Summary: Beyond the Mean: Sequence Analysis Methods for Clustering Ordinal EMA Data

1. Problem Statement

Ecological Momentary Assessment (EMA) generates high-frequency, longitudinal, and often ordinal (e.g., Likert-scale) data. While these data provide rich insights into real-world behavioral and psychological dynamics, they present significant analytical challenges:

Information Loss: Traditional analyses often collapse longitudinal profiles into simple summaries (like the arithmetic mean), which fails to capture temporal patterns, volatility, and state-transition dynamics.
Data Heterogeneity: Participants often have varying numbers of observations and irregular sampling intensities.
Limitations of Existing Latent Models: Standard methods like Latent Class Analysis (LCA) and Latent Transition Analysis (LTA) struggle with high-frequency data, varying time points per subject, and computational intensity as the number of time points increases.
Theoretical Ambiguity: In stress research, competing theories (CATS vs. GUTS) suggest different underlying patterns of stress activation, but current methods lack the flexibility to identify these latent subgroups in complex EMA datasets.

2. Methodology

The authors propose a novel framework that integrates Sequence Analysis (SA) principles with dimensionality reduction and clustering to characterize individual-level temporal patterns.

A. Feature Engineering (Sequence-Inspired Summaries):
Instead of using raw time-series data, the authors transform each individual's longitudinal profile into a vector of informative summary statistics. To capture temporal dynamics, they introduce a lag variable ( $L_{it} = X_{it} - X_{i(t-1)}$ ). The resulting feature set includes:

Central Tendency & Dispersion: Mean stress ( $\bar{X}_{i\cdot}$ ), Standard Deviation of stress ( $SD(X_{i\cdot})$ ), and the Mode.
Temporal Dynamics: Mean of the lag ( $\bar{L}_{i\cdot}$ ), Standard Deviation of the lag ( $SD(L_{i\cdot})$ ), and a measure of temporal stability (the proportion of time where the lag is zero).
Mode Consistency: The probability that an observation matches the individual's mode.

B. Dimensionality Reduction and Clustering:

PCA: Principal Component Analysis is applied to the $N \times (p+1)$ matrix of summary statistics to reduce dimensionality and mitigate multicollinearity.
K-means Clustering: The first two principal components are used as inputs for K-means clustering to identify $K$ latent groups of individuals with similar stress trajectories.

C. Validation and Application:

Simulation: The method was tested against LCA and LTA using a Categorical Functional Regression model across four settings (LCA-friendly, LTA-friendly, noisy, and high-overlap).
Real-world Application: The method was applied to the MyBPLab dataset to cluster stress profiles and evaluate their predictive power regarding cognitive performance (memory test scores) using a Binomial Generalized Linear Mixed Model (GLMM).

3. Key Contributions

Robustness to Irregularity: Unlike LCA/LTA, the proposed PCA-based approach naturally accommodates varying numbers of observations per subject and irregular time intervals.
Stability in Complex Scenarios: The simulation study demonstrates that the PCA-based approach is more stable and consistent than LCA and LTA, particularly in "LTA-friendly" (cyclical) and "high-overlap" settings.
Mitigation of Multicollinearity: By using PCA before clustering, the method avoids the unstable parameter estimates that occur when using raw summary statistics directly in regression models.
Integration of SA and Regression: The framework bridges the gap between qualitative sequence analysis (often used in social sciences) and quantitative regression modeling (used in biostatistics).

4. Results

Simulation Findings: LCA performed best in simple, low-dependence settings. However, LTA failed significantly in high-overlap scenarios, and the PCA-based method emerged as the most reliable across all four simulated environments.
EMA Cluster Characterization: In the MyBPLab data, three distinct clusters were identified:
- Cluster 1 (Stable/Low Stress): High stability, low mean stress.
- Cluster 2 (Volatile/High Stress): High mean stress, high variability, and frequent state transitions.
- Cluster 3 (Intermediate): Moderate stress with moderate fluctuations.
Cognitive Impact: The PCA-based clustering (Model 2) achieved a better model fit (lower AIC) than the "mean-only" model (Model 0), suggesting that the pattern of stress is a more informative predictor of memory performance than the average level of stress alone.

5. Significance

This research provides a scalable and flexible toolkit for researchers working with high-frequency longitudinal data. By moving "beyond the mean," the method allows for the discovery of latent phenotypes in behavioral health—such as identifying individuals who are not just "highly stressed" on average, but "highly volatile" in their stress responses. This has profound implications for personalized medicine and psychological interventions, where the nature of a symptom's trajectory may be as important as its magnitude.