The problem sounds deceptively simple. In any experience sampling study, a proportion of participants will report exactly the same score on a given construct across every measurement occasion. Someone might rate their daily stress as a three on a scale, every single day, for weeks. The authors call these cases non-varying individuals, meaning that their observed scores on certain state constructs remain constant over the study period. Crucially, the researchers emphasize that this label does not imply such people are inherently incapable of change; it describes an observed pattern in the data, which may reflect genuine stability, restricted circumstances, or response habits such as repeatedly choosing the same scale point. Whatever the cause, the statistical consequences are far from trivial.

Luo and colleagues begin with a motivating example drawn from daily stress research, using measures of daily stressors of the kind captured by instruments such as the Daily Inventory of Stressful Events. When they included non-varying individuals in a univariate autoregressive model, the substantive conclusions changed. Autoregressive parameters, which describe how strongly a person’s stress today depends on their stress yesterday, are the backbone of this modeling tradition. A high autoregressive effect suggests a sluggish system that carries perturbations forward, while a low one suggests rapid recovery. The demonstration showed that the simple act of keeping zero-variability participants in the sample could flip what researchers would report about how stress propagates over time.

To understand why, it helps to consider what a constant time series does to an autoregressive estimate. For an individual whose scores never change, the model sees a perfectly predictable series: yesterday’s value fully determines today’s. Depending on how the model handles such cases, these flat trajectories can pull estimated dynamics toward extreme values. The team’s first simulation study, focused on univariate processes, confirmed the mechanism: as the proportion of non-varying individuals in a sample increased, the autoregressive estimates showed a systematic upward bias. In other words, the population would appear more self-predictive, more inertial, than it truly is, purely because some members contributed flat lines rather than genuine fluctuations.

The second simulation extended the investigation to bivariate processes, where researchers estimate not only how a variable predicts itself over time but also how one variable, say stress, predicts another, say negative affect, at the next occasion. These cross-lagged effects fuel countless claims about emotional reactivity, mutual influence between partners, and feedback loops between symptoms. Here the findings were subtler and arguably more alarming. The average, fixed-effect cross-lagged estimates could look accurate on the surface, giving analysts false confidence. Yet beneath that apparent accuracy, the person-specific cross-lagged effects were systematically distorted, with some individuals’ effects overestimated and others underestimated. A researcher examining individual differences in emotional dynamics, or trying to identify who is most reactive, could be badly misled.

Within the widely used Gaussian autoregressive modeling framework, the authors arrive at a clear practical recommendation: estimate dynamic parameters using a subsample that excludes non-varying individuals. This is not a call to discard participants as defective, but a recognition that a flat observed series carries no information about temporal dynamics and can actively inject bias into estimates pooled across people. The recommendation echoes a broader movement in the methodological literature, which has recently scrutinized related data pathologies in intensive longitudinal designs, including floor effects that compress scores against scale minima and zero inflation that floods datasets with identical values. Non-varying individuals represent a distinct and previously understudied facet of this family of problems.

Importantly, the study does not stop at a blanket rule. Luo, Hu, and Liu delineate when subsample estimates can be interpreted as approximations to the full population, and when they should instead be read as describing only the subsample population. Their simulations indicate that in bivariate processes, once the proportion of non-varying individuals reaches around ten percent or more, the dynamics estimated from the varying subsample can no longer be safely generalized to everyone who was recruited. Below that threshold, the subsample estimates serve as reasonable approximations of the whole; beyond it, researchers must be explicit that their conclusions apply to the subset of people whose states actually fluctuated. This distinction matters for fields such as affective science, where claims about population-level emotional dynamics rest on samples that may contain substantial pockets of stability.

The implications ripple across the many domains that have embraced within-person modeling. Researchers have documented intraindividual variability in pain, sleep, perceived stress, affect in older versus younger adults, state academic self-concept among students, and daily sense of purpose, and meta-analytic work on ecological momentary assessment shows the method now spans virtually every corner of psychology. Some of this literature has already grappled with variability itself as a substantive quantity, asking what predicts within-person variance in applied constructs and whether traits like neuroticism relate to emotional instability. The new findings add a methodological caution to that substantive conversation: before interpreting variability, or dynamics, researchers should first examine each individual’s within-person variability and account for those who show none.

The authors also situate their work within a rapidly maturing methodological ecosystem. Dynamic structural equation models, Bayesian multilevel approaches, and related frameworks have made person-specific dynamics routinely estimable, and open resources such as databases of openly available experience sampling datasets are flooding the field with intensive longitudinal data. As data volume grows, so does the chance that non-varying individuals slip through automated pipelines unnoticed. The study’s data and code have been made openly available on the Open Science Framework, allowing applied researchers to reproduce the simulations and apply the recommended screening procedures to their own projects. The work was supported by the National Natural Science Foundation of China, and the authors report no conflicts of interest.

For the practicing scientist, the takeaway is a short checklist with long consequences. Screen every participant’s time series for zero observed variability before fitting dynamic models. Report how many individuals were excluded and why. Interpret autoregressive and cross-lagged estimates from the varying subsample as population approximations only when the excluded fraction is small, and as subsample descriptions when it approaches or exceeds roughly ten percent in bivariate settings. And resist the temptation to treat flat responders as noise to be quietly absorbed; as this study demonstrates, their inclusion can inflate autoregressive estimates and silently scramble person-specific cross-lagged effects even while group averages look pristine. In a research culture increasingly built on the promise of capturing life as it actually unfolds, the people whose numbers never move turn out to be among the most consequential figures in the dataset, precisely because of the stillness they bring to it.

Subject of Research: Statistical handling of non-varying individuals in within-person dynamic modeling of intensive longitudinal data

Article Title: Examining within-person variability of each individual: How should we deal with non-varying individuals?

Article References: Luo, X., Hu, Y., & Liu, H. (2026). Examining within-person variability of each individual: How should we deal with non-varying individuals?. Behavior Research Methods, 58(10), Article 285. https://doi.org/10.3758/s13428-026-03171-1

Image Credits: AI Generated

DOI: 10.3758/s13428-026-03171-1

Keywords: within-person variability, intensive longitudinal data, autoregressive models, cross-lagged effects, dynamic structural equation modeling, ecological momentary assessment, non-varying individuals, simulation study, daily stress, parameter bias, Behavior Research Methods, psychological methods