# What exactly qualifies as intensive longitudinal data and why am I not able to use more traditional growth models to study stability and change over time?

Recent years have seen increasing interest in the collection and analysis of intensive longitudinal data (or ILD) to generate unique insights into within-person processes and change over time. In this post, we first define ILD by contrasting it to data obtained from other common longitudinal designs. Next, we consider the distinct features of ILD that we must address and can leverage in our analyses. Last, we describe two common approaches for analyzing ILD: multilevel modeling and dynamic structural equation modeling.

To start, there is often much confusion over what constitutes intensive longitudinal data (or ILD), in large part because there exists no formal definition that separates ILD from other types of longitudinal data. That said, ILD tends to fall between two traditional data structures obtained from alternative designs: panel data and time series data. It’s useful to first consider these traditional structures to see how several of their features will combine within ILD.

Historically, the most common method for gathering longitudinal data in psychology and the social and health sciences has been the *panel design*. Typically, a panel design involves assessing a large sample of subjects (say 200 or more) at a much smaller number of time points (say three to six) that tend to be widely spaced in time (say six or 12 months or more). Panel data are often used to empirically examine long-term trajectories of change that might span multiple years, and common analytic methods include the standard latent curve model or a multilevel growth model. (See our prior Help Desk entry on the relation between the LCM and MLM).

A second type of longitudinal design, commonly used in economics among other areas, is the *time series* *design*, which resides at the opposite end of the continuum from the panel design. More specifically, a time series design is often based on just a single unit that is repeatedly assessed a very large number of times (say 100 to 200 or more) at intervals that tend to be close together in time (say daily or even hourly). Time series data are often used to empirically examine short-term dynamic processes that might unfold hour-by-hour or day-by-day (e.g., the daily closing cost of the S&P500) and many specialized analytic methods exist to fit models to these highly dense data.

ILD tends to fall between the two extremes of panel data on one end and time series on the other. More specifically, ILD tends to have fewer subjects than panel data but more than time series (say 50 or 100 subjects) and more time points than panel data but possibly fewer than time series (say 30 or 40 assessments). Data might be captured using wearable technology (e.g., heart rate or blood pressure monitors) or by sending random prompts throughout the day via smart phones or other electronic devices (e.g., a tone sounds on a smart phone three times throughout the day and an individual is prompted to respond to a brief feelings survey). As a hypothetical example, a study might be designed to randomly measure nicotine cravings and cigarette use in a sample of 50 individuals four times per day for a two week period resulting in 56 assessments on each individual, thus falling between traditional panel and time series designs in structure.

In the spirit of *be careful what you ask for*, once you obtain intensive longitudinal data you must then select an optimal modeling strategy to test your motivating hypotheses, and this is not always an easy task. To begin, some longitudinal models that we are familiar with from panel data simply will not work with ILD. Consider the latent curve model (LCM): because the LCM is embedded within the structural equation model, each observed time point is represented by a manifest variable in the model. This works well if the model is fit to annual assessments of some outcome (say antisocial behavior at age 6, 7, 8, 9 and 10) where each age-specific measure serves as an indicator on the underlying latent curve factor. However, the LCM rapidly breaks down with higher numbers of repeated measures in which only one observation may have been obtained at any given assessment (e.g., 9:15am, 9:52am, and so on). For our prior example with 56 repeated assessments taken on 50 subjects, the LCM is simply not an option.

We can next consider the multilevel model (MLM) and it turns out that this option works quite well for many ILD research applications. (See our Office Hours channel on YouTube for a lecture on the MLM with repeated measures data). The MLM approaches the complex ILD structure as nested data in which repeated assessments are nested within individual. Interestingly, unlike the standard LCM, the MLM can be applied to both more traditional panel data and to ILD. The reason is that, whereas the LCM incorporates the passage of time into the factor loading matrix and requires an observed variable at each assessment, the MLM incorporates the passage of time as a numerical predictor in the regression model. As such, the MLM can easily allow for highly dense (meaning many time points) and highly sparse (meaning few or even one assessment is shared by any individual at any given time point) data without problem. (The LCM can under certain circumstances be contorted to accommodate some of these features as well, but the MLM does this seamlessly). However, there are several complications that must be addressed when fitting an MLM to intensive longitudinal data that do not commonly arise in panel data.

The first issue is what is called *serial correlation* of the residuals for the repeatedly measured outcome. With apologies for the technical terminology, this means is that for a given person, when there is a “bump” at one timepoint, that tends to carry over to the next time point too. For instance, say a person’s average heart rate is 72 BPM. I measured this person at 9:10am and 9:26am. What I don’t know is that this person was late for their 9:00am job, which lead them to move faster and increased their stress, and they had only just arrived at 9:10am. This manifested in a heart rate of 91 BPM at 9:10 and 83 BPM at 9:26. The initial bump has thus not entirely dissipated by the second assessment.

Serial correlation is often not of importance in panel data because these perturbations have long since washed out (the residual correlation goes to zero over the long lags). A person’s heart rate might be higher than usual when I assess them at age 26 because they had a second shot of espresso or got in an argument with a colleague at work, but the effect of the espresso or argument has long since worn off by the time I reassess them at age 27. Of course, even with panel data the repeated measures are correlated, but not because of serial correlation of within-person *residuals* but because of individual differences in level and change over time. For instance, some people have consistently higher heart rates and others have consistently lower heart rates and this stability will lead to across-person positive correlations in repeated measures. We typically model these individual differences in level and change via latent growth factors / random effects when fitting LCMs / MLMs. Such individual differences may be an important source of correlation in ILD too, but we also have to contend with the serially correlated residuals. Although an added complexity, the MLM is quite well suited at incorporating serial correlations such as these. Complex error terms can be defined among the time-specific residuals such as auto-regressive, Gaussian decay, spatial power, or Toeplitz structures. It is very important these serial correlations be represented in the model if needed both to gain insights into the phenomenon under study and to ensure that other parameter estimates of interest are not biased.

A second issue that often arises in ILD is the presence of cycles or transition points that might occur during the assessment period. For example, daily measures taken over several weeks may vary as a function of weekday vs. weekend (e.g., if studying college drinking) or might cycle regularly throughout a day (e.g., hourly heart rate data varying as a function of waking to sleeping and back to waking). Although such cycles and transition points might be present in panel data as well, these are less likely to occur because there are typically fewer time-linked assessments and these tend to aggregate over longer durations (e.g., if we ask “over the past 30 days” to obtain monthly alcohol use levels, these ratings will implicitly smooth over weekday-weekend differences in daily alcohol use). In contrast, multiple cycles might be observed in ILD spanning a 50 or 60 time point series.

Finally, a third issue is the distinction between within- versus between-person effects. Often ILD is collected with the idea of assessing processes as they unfold in real time for individual participants (“life as lived”). For instance, we might be interested in using ILD to test a negative reinforcement hypothesis for alcohol use. That is, we wish to test the proposition that people drink more than they typically do when they are experiencing increased negative affect under the expectation that this will reduce their negative affect. Using a daily diary study, we measure negative affect each day and alcohol use each night and we build a model to predict alcohol use from negative affect. To fully assess the negative reinforcement hypothesis, we must differentiate the within-person effect (e.g., when my negative affect is higher than usual I drink more than is typical for me) from any between-person correlation that may also exist (e.g., that people who have higher negative affect in general tend to drink more in general). Fortunately, with the MLM we have well developed methods for separating within- and between-person effects, although there are some complications to consider (see our prior help desk post specifically on this issue)

The MLM is thus well suited to address all of these complexities that commonly arise in intensive longitudinal data. Once incorporated, the MLM offers many of the very same advantages as when applied to panel data: time-varying predictors can be incorporated at level-1 with either fixed or random effects, time invariant predictors can be incorporated at level-2, and interactions can be estimated within or across levels of analysis. However, there are two key limitations of the MLM that may or may not arise in a given application. The first is that, similar to the traditional general linear model, the MLM assumes all measures are error-free and all observed variance is “true” variance. This is often (if not always) an unrealistic assumption and violation of this assumption can lead to significant biases in the estimated results. The second is that the MLM only allows for one dependent variable at a time and is thus limited to the estimation of unidirectional effects. Say that you are interested in testing the reciprocal relations between depression during the day and substance use that evening, and you obtain multiple daily measures spanning a week of time. The MLM allows for the estimation of the prediction of substance use from depression, but not the simultaneous estimation of the reciprocal prediction of depression from substance use. As such, the MLM is only evaluating one part of the research hypotheses at hand.

However, recent developments have introduced a new analytic procedure that combines elements of the MLM, the SEM, and time series models called the dynamic structural equation model (or DSEM). The DSEM functionally picks up where the MLM leaves off, but expands the model to potentially include latent factors (to estimate and remove measurement error) and multiple dependent variables (to estimate reciprocal effects between two or more variables over time). DSEM is a recent development and much has yet to be learned about best practices in applied research settings, but it represents a significant development in our ability to fit complex models to ILD.

Want to learn more? We recently had the honor of being invited to provide a series of three lectures on intensive longitudinal data analysis for the American Psychological Association and we have posted our lecture materials in the resources section of the CenterStat home page (https://centerstat.org/apa-ild/). The first session discusses the challenges and opportunities of ILD; the second focuses on the analysis of ILD using the multilevel model; and the third focuses on the analysis of ILD using the dynamic structural equation model. In addition to those resources, below are several suggested readings on the design, collection, and analysis of intensive longitudinal data. Asynchronous access to CenterStat workshops on *Multilevel Modeling** *and *Analyzing Intensive Longitudinal Data* is also available to those who might wish to register for additional training. You can also check our workshop schedule for upcoming live offerings.

Good luck with your work!

Asparouhov, T., Hamaker, E. L., & Muthén, B. (2018). Dynamic structural equation models. Structural Equation Modeling: *A Multidisciplinary Journal, 25*, 359-388.

Asparouhov, T., & Muthén, B. (2020). Comparison of models for the analysis of intensive longitudinal data. *Structural Equation Modeling: A Multidisciplinary Journal, 27*, 275-297.

Bolger, N., & Laurenceau, J. P. (2013). *Intensive longitudinal methods: An introduction to diary and experience sampling research*. Guilford Press.

Hamaker, E. L., Asparouhov, T., Brose, A., Schmiedek, F., & Muthén, B. (2018). At the frontiers of modeling intensive longitudinal data: Dynamic structural equation models for the affective measurements from the COGITO study. *Multivariate Behavioral Research, 53*, 820-841.

Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. Routledge.

McNeish, D., & Hamaker, E. L. (2020). A primer on two-level dynamic structural equation models for intensive longitudinal data in Mplus. *Psychological Methods, 25*, 610-635.

McNeish, D., Mackinnon, D. P., Marsch, L. A., & Poldrack, R. A. (2021). Measurement in intensive longitudinal data. *Structural Equation Modeling: A Multidisciplinary Journal, 28*, 807-822.

Walls, T. A., & Schafer, J. L. (Eds.). (2006). *Models for intensive longitudinal data*. Oxford University Press.