Causal cycles,causal intervals,and measurement in over-time studies

Abstract

If over-time data are used to model XàY causal relationships, the measurement (or “recording”) interval should match (or at least approximate) the actual causal (or “existence”) interval for X’s effect on Y. I discuss this issue in the context of causal cycles of events and give three examples involving hurricanes, job change and adoption and implementation of new technology. I conclude with some considerations and recommendations for matching measurement to causal intervals in over-time research.

Once upon a time, when empirical articles in IO psychology were short and to the point and didn’t drip from thick layers of theory (Hambrick, 2007), an ultimate goal of Future Research was to collect multivariate longitudinal data (MVLD) in order to REALLY answer the burning questions of the day (e.g., Dunnette, 1963). Never mind that no one had a clue as to how to analyze and understand MVLD. Still, it was a noble cliché. ¹

But why MVLD? Because MVLD are accepted as being better than cross-sectional (XS) data – a received doctrine that Spector (2019) referred to as a “universal condemnation of the cross-sectional design and…acceptance of the superiority of the longitudinal design” (p. 125). Unlike XS data, MVLD permit examination of relationships among multiple variables simultaneously, and allegedly support the drawing of causal conclusions from the data.

Causality is a WAY complicated issue, ² but one often-cited holy trinity for establishing causality is (a) the cause (X) must be related to the effect (Y) (both XS and MVLD readily do this), (b) temporal precedence must be established for X over Y (allegedly, MVLD trumps XS data here), and (c) (all) other explanations for Y must be ruled out (this is a tough one for both XS and MVLD).

Today, several U.S. Presidents since the GODs, MVLD are more common, and we have a plethora ³ of methodologies for analyzing and making sense of MVLD, including multilevel modeling (González-Romá & Hernández, 2023; Hox et al., 2017), many variations on latent growth modeling (Grimm et al., 2017; Little, 2013), latent difference score modeling (McArdle, 2009), various Latent State-Trait models (Geiser et al., 2020), and very good arguments can be made for how and why our fields have genuinely advanced using these more sophisticated data collection designs and analytic techniques (Hair et al., 2018).

But MVLD also pose additional challenges compared to XS research, one of the most critical being the timing of the data collection. Returning to the temporal precedence issue, the basic (and very naïve) idea is that any difference in the size of the relationship between X measured before Y, versus Y measured before X, informs on the temporal precedence between X and Y themselves. That is, if the relationship between X (Time t) and Y(Time t + 1) is greater than the Y(Time t)–X (Time t + 1) relationship, then X→Y and not Y→X. Easy, huh? Not so. ⁴ This establishes only that X and Y as measured relate in such and such way, not necessarily that X and Y are themselves related in the same way. This distinction points to the concern raised here: correspondence between X and Y as measured (the “recording interval”) relative to the natural causal cycle between X and Y (the “existence interval,” Zaheer et al., 1999).

James et al. (1982, “JMB”) and Mitchell and James (2001) describe a causal cycle as consisting of (a) an equilibration period, during which time the cause (X) exerts its effect on the outcome (Y), and during which Y is in flux and changing, (b) an equilibrium-type condition, during which time X’s effect on Y has been realized, Y has stabilized, and now exists in a “temporary state of approximate constancy” (JMB p.49), and (c) an entropic period, during which X’s effect on Y dissipates, and changes in Y are decreasingly a function of X’s previous influence (see Figure 1, adapted from Mitchell & James). What’s important here are the lengths of the (a) causal interval (equilibration period), (b) equilibrium-type condition, and (c) entropic period, relative to when X and Y are measured.

Figure 1.

A hypothetical casual cycle between X and Y.

An Example

Take, for instance, a scenario with which many residents of the southeastern United States are, unfortunately, far too familiar. A hurricane (X) with measured barometric pressure and maximum sustained winds and gusts bears down on the coast, its winds, rain and tidal surge razing buildings, unmooring watercraft, uprooting trees, sending palm fronds and stray cats flying through the air, flooding lower-lying areas, etc. (all indicators of Y, storm damage). This is the equilibration period, the time during which the hurricane is unleashing its wrath on the coastal environs. Surely, this would be too early to assess damage because it’s still occurring and accumulating. Next, the hurricane passes along to the next unfortunate locale, leaving casualties, property loss, disruption in infrastructure and utility services, missing cats, water and food shortages, etc. Soon, first responders arrive, human and feline survivors are rescued, utilities and access to the affected areas begin to be restored. At this point, there is a window of opportunity during which the hurricane’s destruction can be assessed before reparations commence in earnest. This is the equilibrium-type condition. Eventually, roads are repaired, buildings are restored, stores are restocked, watercraft are scuttled or salvaged and re-moored, the resident cat population rebounds, the environs are re-landscaped etc., and life returns to some semblance of normality. This is the entropic period. Now would be too late to assess X’s damage after the environs’ restoration is well underway, for the effect of the hurricane would be dissipating as the extent of storm damage (Y) becomes less evident over time.

The key here is that in assessing causal effect of storm strength (X) on damage incurred (Y), X should be assessed prior to, and Y should be assessed during the equilibrium-type period, before restoration commences at the beginning of the entropic period. Measuring X while X is still exerting its effect on Y would underestimate the X→Y relationship as X’s effects have not been fully realized yet. Measuring Y long into the entropic period would also underestimate the X→Y relationship as X’s effects will have diminished. This is what authors hint at when they say that “the challenge is to ensure that the lag is not too short or too long” (Ployhart & Vandenberg, 2010, p. 104).

Causal Cycles and Events

Causal cycles can be viewed as describing connections between X(s) and Y(s) involved in corresponding events: “discrete, discontinuous happenings which diverge from the stable or routine features of the organizational environment” (Morgeson et al., 2015, p. 519). Hurricanes are HUGE events, each one unique in its strength, duration and permanence of its effects, as are earthquakes and organizational collapses. Work hassles, though not necessarily trivial, are more minor, perhaps recurring, whose effects may soon dissipate, returning workers’ stress levels toward some default level, or “set point” (Headey & Wearing, 1989; Lucas, 2007). Other events (e.g., voluntary turnover) may involve multistage causal cycles (thinking of quitting, job search) nested within the singular molar event (Hom et al., 2017). Still other events occur at more macro levels, including team-, business unit-, organizational-, and (inter)national-level events (Liu et al., 2023). The challenge is to understand the causal cycles associated with these very different events and design data collection accordingly.

So How are We Doing?

That’s a BIG question. As just one micro-level example, one area of work-family research concerns how work stressors lead to perceptions of work-family conflict, affective reactions, somatic complaints, and myriad ⁵ other stuff (Allen & French, 2023). Allen et al.’s (2019) review of over-time work-family studies differentiated between lagged (prospective), longitudinal, and experience sampling (ESM or diary) studies. The modal measurement interval of the 40 longitudinal studies with at least three measurement waves was 6 months (does X→Y really take six months?). Only 6 of these 40 studies provided a rationale for the lag length, citing “previous empirical work or logic that suggested how much change might be expected in variables over time” (p. 249). So it seems that not much attention has been paid to the issues raised here in longitudinal studies. However, turning to the more recent k = 37 ESM studies, the prototypical study obtained daily measures before bedtime (some upon waking or after work) for 5 (k = 10) or 10 (k = 9) consecutive work days, taking work day as a naturally-occurring work-family conflict cycle. Allen et al. stressed the importance of “issues such as how long does a phenomenon such as work-family conflict last in a steady state, when does work-family conflict begin and end, and what are the trajectories...over time” (p. 251), and it seems that recent ESM studies are beginning to do just that, designing data collection intervals to correspond to series of multiple causal cycles (days or workweeks) involving work-related challenges and stressors (Xs) and employees’ corresponding reactions to them (Ys).

Two Other Examples

In contrast to relatively “shortitudinal” (Dormann & Griffin, 2015) work-family ESM studies literature, two other examples illustrate what can be done to map data collection intervals onto causal cycles with vastly different event durations.

The first example is an intermediate-duration event: job change as related to newcomer socialization and “honeymoon effects” in job satisfaction (Boswell et al., 2005). Starting a new job can be associated with initial favorable views of the new employer, followed by changes associated with accrued organizational experiences. Boswell et al. obtained assessments at an orientation session on Day-1 of employment followed by additional assessments 3, 6 and 12 months later based on previous research and on “insight on the basis of the organization’s director and human resource manager” (p. 848) as to typical transition and socialization points in the organization. They found evidence of “honeymoon effects” in which initial favorable organizational perceptions gradually dissipated as employees eventually asymptoted toward their “set points” as organizational experiences became more routine (Lucas, 2007, the entropic period in Figure 1).

A second example is much more macro, both in terms of level and duration. Using discontinuous growth modeling of archival data obtained over the course of 10+ years from 87 units of a Fortune 200 multinational firm, Flynn et al. (2024) assessed unit-level changes in energy consumption 12 months prior to and 12 months following the installation of real-time energy consumption monitoring technology (“smart meters”). The installation itself (the event-X) varied in duration across units from 1 to 108 months. The amount of reduction in energy consumption (Y) also varied significantly across units, as was predicted by unit differences in event duration (time to complete smart meter installation), criticality (extent to which unit managers actually monitored smart meter data) and timing (date at which installation began). Thus, this extensive data collection effort captured run-up, change and follow-through, or “pre-event, in-event, and post-event dynamics” (Liu et al., 2023), corresponding in a macro sense to the change cycle stages in Figure 1.

So…

Don’t collect data X-ually just because everybody else does (you know better than that, right?). Understand the phenomena (events) that you study as best you can. Ask people imbedded in those kinds of events what’s going on because they know better than you do. There may well exist “natural” causal cycles such as a work day-in-the-life (Lennon & McCartney, 1967). Recognize different possible forms of change such as long-term “developmental trends,” shorter-term perturbations and fluctuations (“swells,” e.g., job change), and more momentary daily, weekly or sporadic “tremors” whose effects may dissipate rapidly (Lumsden, 1977). As such, Figure 1’s timeline could refer to a lifetime, 5 years of grad school, a work week or even the few seconds following the Zoom call you just finished. Consider that for some event systems with short equilibration times and relatively enduring, stable equilibrium-type states, XS data may be appropriate, and perhaps even more so, than over-time data (Spector, 2019, see JMB “Condition 7”) Keep abreast of ongoing work to identify optimal data collection intervals for certain (types of) events (e.g., Dormann et al., 2020; Dormann & Griffin, 2015; Ford et al., 2014; Nohe et al., 2015; Zhou et al., 2021), as this may well relate to your stuff. And adopt an advocacy stance (Rice, 2022) to argue for why what you did was appropriate ⁶ . Doing science is hard, isn’t it?