pith. sign in

arxiv: 2604.23834 · v1 · submitted 2026-04-26 · 📊 stat.ME · stat.AP

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

Tianyi Wang , Anna L. Smith , Jillian R. Silva-Jones , Wendy Berry Mendes , Lauren N. Whitehurst This is my paper

Pith reviewed 2026-05-08 05:49 UTC · model grok-4.3

classification 📊 stat.ME stat.AP
keywords ecological momentary assessmentsequence analysisclusteringordinal datalatent profilesstresscognitive performance
0
0 comments X

The pith

Sequence analysis of ordinal EMA stress ratings identifies latent profile groups that better characterize effects on cognitive performance than mean summaries alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes borrowing measures from sequence analysis to summarize temporal patterns across repeated ordinal ratings in ecological momentary assessment data. These measures are then processed through principal component analysis and K-means clustering to recover unobserved groups of individuals who share similar stress trajectories over time. The approach is tested on simulated data from a categorical functional regression model against latent class analysis and latent transition analysis, then applied to real stress EMA observations from a large U.S. adult sample. Distinct latent stress profile groups emerge that improve the characterization of stress impacts on cognitive performance beyond what average stress levels can capture. A sympathetic reader cares because many EMA studies rely on simplified averages that discard dynamic information, and recovering meaningful temporal groupings could refine how daily experiences are linked to outcomes.

Core claim

We borrow sequence analysis measures to capture individual-level patterns over time in ordinal EMA profiles, apply PCA followed by K-means clustering to identify latent groups, and demonstrate using stress observations that these groups improve characterization of impacts on cognitive performance relative to mean-based summaries.

What carries the argument

Borrowed sequence analysis measures that quantify temporal patterns in ordinal sequences, reduced by principal component analysis and partitioned by K-means clustering to form latent profile groups.

If this is right

  • The clusters serve as improved predictors in downstream models relating stress to cognition.
  • The method handles varying observation counts per individual without requiring balanced panels.
  • It provides an alternative to latent class analysis and latent transition analysis for detecting group structure in ordinal longitudinal data.
  • Distinct profile groups allow finer characterization of how different stress trajectories affect performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same pipeline could be tested on other ordinal EMA domains such as mood or pain to see whether temporal clustering reveals similar gains over averages.
  • If the identified groups prove stable across studies, they might support targeted interventions that address specific daily stress patterns rather than overall stress levels.
  • Comparing multiple sequence distance metrics within the same data could reveal which aspects of temporal ordering matter most for the cognitive links.

Load-bearing premise

The sequence analysis measures adequately summarize the relevant temporal dynamics in the ordinal EMA profiles, and the resulting clusters reflect meaningful latent structures rather than artifacts of the chosen metrics or algorithm.

What would settle it

If cluster membership derived from the sequence measures shows no added predictive value for cognitive performance outcomes after accounting for average stress levels, or if the groups fail to replicate in a held-out sample of EMA data.

Figures

Figures reproduced from arXiv: 2604.23834 by Anna L. Smith, Jillian R. Silva-Jones, Lauren N. Whitehurst, Tianyi Wang, Wendy Berry Mendes.

Figure 1
Figure 1. Figure 1: Memory test from MyBPLab data (Silva-Jones et al., 2025; Gilmore et al., 2024). There are two photo-word sets; each learning session is followed by three test sessions on different days. . . . . . . . . . . . . . . . . . . t1 t2 t3 t8 t9 t10 t17 t18 t19 T − 1 T Stress Rating Memory Test view at source ↗
Figure 2
Figure 2. Figure 2: An example timeline for memory tests and stress rating observations. Red and blue arrows indicate timepoints at which memory tests and stress ratings are recorded, respectively. 3 Existing approaches Our goal is to explain how participants’ self-reported stress levels impact their cognitive performance on the memory tests, while incorporating the high frequency of stress reports available in the data, and … view at source ↗
Figure 3
Figure 3. Figure 3: Sequence index plot (left: 20 individuals, maxi Ti ≈ 70; right: all individuals, maxi Ti ≈ 1750). Each color represents a distinct stress state. This figure is created using the plotData function from the cfda package (Preda et al., 2021). In our data, each horizontal row represents an individual’s stress states over time. Each block indicates a specific stress level at a given time point, with different c… view at source ↗
Figure 4
Figure 4. Figure 4: 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 time state view at source ↗
Figure 5
Figure 5. Figure 5: Simulation results: the multi-panel plot displays Recall, Accuracy, Precision, and the Estimate-to-True Size Ratio. Rows represent the four settings: LCA-friendly, LTA-friendly, LCA-friendly+Noise, and More Overlap. Columns distinguish between the internal transition matrices (L1, L2, and L3). Colors indicate group-specific sample size. Clusters (k) SD(Xi.) X¯ i. L¯ i. SD(Li.) P(Lit = 0) T¯ i Modei P(Modei… view at source ↗
Figure 6
Figure 6. Figure 6: Distribution of individual mode by cluster: Each panel represents a latent cluster (K = 3) estimated by our P CA−based approach, where the bars indicate the frequency of the most common response value (mode) for individuals within that group. We also checked the appropriate number of principal components by examining the scree plot. As shown in the scree plot ( view at source ↗
Figure 7
Figure 7. Figure 7: Longitudinal stress and lag trajectories by cluster. Each column presents data for 25 randomly selected individuals from each cluster (K = 3), identified via our PCA-based approach. The top row illustrates reported stress levels over time, while the bottom row depicts change in consecutive stress score. To maintain visual interpretability and prevent scaling imbalances caused by high-frequency responders, … view at source ↗
Figure 8
Figure 8. Figure 8: GLMM regression results across five model specifications. The table presents estimated coefficients and standard errors (in parentheses) for each model. Model 0 serves as the reference using mean stress. Model 1 incorporates the full set of informative summary statistics, while Model 2 represents the PCA-based K-means cluster. The sensitivity analysis are provided by Models 3 and 4 represents fuzzy (C-mean… view at source ↗
Figure 9
Figure 9. Figure 9: Correlation of informative summary statistics: This heatmap displays the pairwise Pearson correlation coefficients among the informative summary statistics derived from longitudinal stress trajectories. Color intensity reflects the strength and direction of the correlation, with darker shades indicating stronger positive (blue) or negative (red) associations. The x- and y-axes represent the different summa… view at source ↗
Figure 10
Figure 10. Figure 10: Scree Plot of Principal Components. This plot displays the percentage of total variance explained by each principal component. A distinct “elbow” is observed at the second component, after which the marginal gain in explained variance reduces dramatically. sd.no1 mean.no1 mean.lagN1 sd.lagN1 percent.lag0 mode_score mode_freq −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 Dim1 (60.8%) Dim2 (19.2%) Loadings of… view at source ↗
Figure 11
Figure 11. Figure 11: Principal Component Loading Plot. This factor map illustrates the relationship between the informative summary statistics defined in Algorithm 1 of the main text. and the first two principal components. PC1 (Dim1, 60.8%) and PC2 (Dim2, 19.2%) together capture 80% of the total variance. The vectors represent the direction and strength of each statistic’s contribution to these dimensions. 21 view at source ↗
read the original abstract

Ecological momentary assessment (EMA) ratings are widely used in studies of behavioral and psychological phenomena to capture real-time data in subjects' real-world environments. Because the data are collected repeatedly over the study period, they provide rich longitudinal rating profiles for each individual. However, the number of observations per subject is often large, while both sample size and sampling intensity can vary substantially across individuals, which complicates the analysis. In some settings, simplified summaries of individual profiles, such as averages computed across the study period, are used for downstream analyses, including regression-style modeling. Although such summaries can be convenient, they may fail to fully capture dynamic temporal patterns present in the complete longitudinal profiles. To address this, we borrow measures from sequence analysis that capture individual-level patterns over time and then applied principal component analysis (PCA) followed by $K$-means clustering to identify unobserved latent groups of individuals with similar profiles. We test our approach using simulated data from a categorical functional regression model and compare its performance with two commonly used methods for detecting unobserved group structures: latent class analysis (LCA), and latent transition analysis (LTA). Using EMA stress observations from a large sample of U.S. adults (Newman et al., 2024, 2025), we identify distinct latent stress profile groups and show that they improve characterization of the impact on cognitive performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces a pipeline for clustering ordinal EMA data by applying sequence analysis measures to capture temporal patterns in individual profiles, followed by PCA and K-means to identify latent groups. It evaluates this method against LCA and LTA using simulations from a categorical functional regression model, and demonstrates its application on real EMA stress data from a large U.S. adult sample, claiming that the resulting groups provide improved characterization of effects on cognitive performance compared to mean-based summaries.

Significance. If the results hold, the method offers a promising extension beyond mean summaries for handling variable-length longitudinal EMA data, potentially leading to more nuanced understanding of dynamic stress profiles and their cognitive impacts. Strengths include the use of established sequence analysis tools, simulation-based validation of group recovery, and a real-world application. However, the significance is tempered by the need for rigorous validation to ensure the clusters capture genuine structure rather than artifacts.

major comments (2)
  1. [Abstract] Abstract and real-data analysis: The central claim that the identified stress profile groups 'improve characterization of the impact on cognitive performance' is based on regressions using clusters derived from the full EMA sequences in the same sample. This risks inflated improvement metrics because the data-driven partitioning is not accounted for in inference. The simulation study validates recovery of known groups but does not replicate the two-stage real-data workflow or test whether the downstream improvement survives out-of-sample validation (e.g., clustering on training subset only).
  2. [Simulation study] Simulation study: While the categorical functional regression model tests group recovery, it does not evaluate the full pipeline's effect on cognitive performance modeling when clustering is performed on a training subset and assessed on held-out data. This leaves the real-data claim that groups add explanatory power beyond means untested against the risk of selection-induced bias.
minor comments (1)
  1. [Abstract] The abstract supplies no quantitative performance metrics, simulation details (e.g., recovery rates, sample sizes), or real-data results (e.g., cluster sizes, R² gains), making it impossible to assess the strength of the comparisons or improvements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's report. We appreciate the referee's careful reading and the insightful comments on the validation of our proposed method, particularly concerning the real-data analysis and simulation design. We provide point-by-point responses below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and real-data analysis: The central claim that the identified stress profile groups 'improve characterization of the impact on cognitive performance' is based on regressions using clusters derived from the full EMA sequences in the same sample. This risks inflated improvement metrics because the data-driven partitioning is not accounted for in inference. The simulation study validates recovery of known groups but does not replicate the two-stage real-data workflow or test whether the downstream improvement survives out-of-sample validation (e.g., clustering on training subset only).

    Authors: We agree that this is a valid concern. Performing clustering on the full sample and then regressing cognitive performance outcomes on the resulting groups within the same data can introduce selection bias and produce inflated estimates of improvement over mean-based summaries. The simulation study is limited to assessing recovery of known groups under the categorical functional regression model and does not simulate the complete two-stage pipeline with held-out evaluation of downstream regression performance. In the revised manuscript, we will add an explicit limitations discussion qualifying the real-data claims as descriptive rather than providing formal inference that accounts for the clustering step, and we will suggest out-of-sample validation strategies for future work. revision: yes

  2. Referee: [Simulation study] Simulation study: While the categorical functional regression model tests group recovery, it does not evaluate the full pipeline's effect on cognitive performance modeling when clustering is performed on a training subset and assessed on held-out data. This leaves the real-data claim that groups add explanatory power beyond means untested against the risk of selection-induced bias.

    Authors: This comment correctly identifies a scope limitation of the simulation. While the simulation demonstrates that sequence analysis metrics followed by PCA and K-means can recover groups more effectively than LCA or LTA under the data-generating process, it does not extend to evaluating how the full pipeline affects explanatory power in a cognitive performance regression when clustering is restricted to a training subset. We will revise the simulation section to clarify its intended scope and will incorporate a discussion of selection-induced bias risks when interpreting the real-data results, along with recommendations for cross-validation in applied settings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies external measures and standard clustering to independent outcome

full rationale

The paper borrows sequence analysis measures from the literature, applies PCA followed by K-means to cluster ordinal EMA stress profiles, validates recovery via simulation under a categorical functional model, and then uses the resulting groups to characterize associations with a separate cognitive performance outcome in real data. No equation reduces a claimed result to its own inputs by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise depends on self-citation chains or imported uniqueness theorems. The downstream regression step treats clusters as an observed covariate rather than deriving the outcome from the clustering process itself. This workflow remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work applies established statistical techniques without introducing new free parameters, axioms, or invented entities.

axioms (1)
  • domain assumption Standard assumptions underlying PCA, K-means, and sequence analysis measures hold for the derived ordinal EMA profiles.
    Implicit in the application of these methods to the data.

pith-pipeline@v0.9.0 · 5554 in / 1033 out tokens · 50553 ms · 2026-05-08T05:49:12.428217+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

  1. [1]

    Place: US

    doi: 10.1037/0033-2909.133.5.761. Place: US. A. S. Cain, A. J. Epler, D. Steinley, and K. J. Sher. Stability and Change in Patterns of Concerns Related to Eating, Weight, and Shape in Young Adult Women: A Latent Transition Analysis.Journal of abnormal psychology, 119(2):255–267, May 2010. ISSN 0021-843X. doi: 10.1037/a0018117. URLhttps://www.ncbi. nlm.nih...

    work page doi:10.1037/0033-2909.133.5.761 2010

  2. [2]

    doi: 10.1177/0049124109357535

    ISSN 0049-1241, 1552-8294. doi: 10.1177/0049124109357535. URLhttps://journals.sagepub.com/ doi/10.1177/0049124109357535. E. S. Epel, A. D. Crosswell, S. E. Mayer, A. A. Prather, G. M. Slavich, E. Puterman, and W. B. Mendes. More than a feeling: A unified view of stress measurement for population science.Frontiers in Neu- roendocrinology, 49:146–169, Apr. ...

    work page doi:10.1177/0049124109357535 2018

  3. [3]

    URLhttps://www.frontiersin.org/journals/sleep/articles/ 10.3389/frsle.2024.1359723/full

    doi: 10.3389/frsle.2024.1359723. URLhttps://www.frontiersin.org/journals/sleep/articles/ 10.3389/frsle.2024.1359723/full. M. Greenacre, P. J. F. Groenen, T. Hastie, A. I. D’Enza, A. Markos, and E. Tuzhilina. Principal compo- nent analysis.Nature Reviews Methods Primers, 2(1):1–21, Dec. 2022. ISSN 2662-8449. doi: 10.1038/ s43586-022-00184-w. URLhttps://www...

    work page doi:10.3389/frsle.2024.1359723 2024

  4. [4]

    doi: 10.1016/j.ejphar.2007.11.071

    ISSN 0014-2999. doi: 10.1016/j.ejphar.2007.11.071. URLhttps://www.sciencedirect.com/science/ article/pii/S0014299908000277. B. S. McEwen. Neurobiological and Systemic Effects of Chronic Stress.Chronic Stress, 1:2470547017692328, Feb. 2017. ISSN 2470-5470. doi: 10.1177/2470547017692328. URLhttps://doi.org/10.1177/ 2470547017692328. A. M. Mournet and E. M. ...

    work page doi:10.1016/j.ejphar.2007.11.071 2007