Emotional Reactivity to Daily Stressors: Does Stressor Pile-Up Within a Day Matter for Young-Old and Very Old Adults?

Abstract

Over the past decade, many studies have reported individual differences in negative emotional reactions to daily stressful events. However, whether and how individual and age-related differences in emotional reactivity also depend on the temporal characteristics of stressors has received little attention. In this project, we focused on the temporal characteristics of stressor occurrence and examined the pile-up of stressors within a day – referring to multiple stressors encountered within a relatively narrow time window. To do so, we used data from 123 young-old (66–69 years, 47% women) and 47 very old adults (84–90 years, 60% women). Participants reported their momentary feelings and exposure to stressors six times a day over seven consecutive days in their everyday life. Emotional reactivity to stressor pile-up over the day followed an exponential decay trajectory, with higher stressor burden in close proximity to the stressor occurrence. The exact shape of the decay trajectory differed among participants. Most importantly, both stressor pile-up and ongoing stress predicted greater emotional reactivity. We also found interaction effects of stressor pile-up and current stressor occurrence in that increases in negative affect under ongoing stress were stronger when stressors had piled-up before. No evidence was found for increased vulnerability to stressor pile-up in very old adults; rather, the impact of preceding stressors attenuated faster for individuals in this age group. The findings highlight the utility of comprehensively studying how stressor characteristics such as their pile-up within short time periods shape emotional reactivity.

Findings from numerous studies suggest that individuals differ greatly in how they emotionally react to daily stressors. Importantly, stable individual differences in the intensity of negative emotions in response to daily stressors are associated with individual differences in long-term mental and physical health (e.g., Almeida, 2005; Charles, 2010; Charles et al., 2013; Hamilton & Miller, 2016; Piazza et al., 2013). Thus, emotional reactivity to daily stressors may signal obstacles for healthy aging and has resulted in efforts to gain an in-depth understanding of older adults’ emotional reactions to daily stressors, as well as understanding age-related changes in emotional reactivity (Schilling & Diehl, 2015). In contrast to this strong research interest, short-term variations in the intensity of emotional reactions to daily stressors are still not well understood. If considered over a week or two, a person’s emotional reactions to stressors can vary from very strong to weak. This within-person variability arguably occurs in part because daily stressors differ greatly in aspects such as predictability, complexity, and severity. For example, past work has suggested that the stressors’ complexity and heterogeneity amplify emotional reactions, particularly in very old individuals (Brose et al., 2013; Wrzus et al., 2013).

What has rarely been considered is whether the temporal spacing of stressor occurrences may also play a role for the strength of emotional reactions. Typically, stressful events and daily hassles do not occur evenly spread over time, but may occur rather erratically and may pile up at times (e.g., Almeida et al., 2002). If a person has to deal with several stressors within a relatively narrow time window, components of the stress process (exposure, reaction, and recovery) may overlap. Perhaps most critical, if an individual is still in the process of coping with an earlier stressor (e.g., a conflict with a family member) while a new stressor occurs (e.g., dealing with a health-related incident), their capacity to handle the new stressor may be limited. Thus, this person’s negative affect in response to the new stressor may be greater than if this stressor had occurred just by itself. This consideration may apply in particular when multiple stressors occur within a day, only a few hours apart, and without a nighttime recovery period between the stressor occurrences.

Given these considerations, both between-person differences and within-person variation in emotional reactivity to daily stressors may not only be shaped by the coupling between a discrete stressor at a given point in time and the concurrent emotional outcome, but also by the stressor burden that has piled-up by the time of assessment. The main goal of this study was to investigate whether and how within-day pile-up of stressors predicts the intensity of daily negative emotional reactions in young-old and very old age. The focus was on stressor pile-up within a day rather than across days (Bolger et al., 1989; Fuller et al., 2003; Grzywacz & Almeida, 2008; Schilling & Diehl, 2014; Smyth et al., 2018). Given the current state of research on this topic, we first addressed the concept and methodological operationalization of reactivity to within-day stressor pile-up. We then used this concept to examine the general degree of and inter-individual differences in reactivity to stressor pile-up in a sample of older adults. In addition, we also tested whether and how emotional reactivity and stressor pile-up differed between young-old and very old adults.

Emotional Reactivity to Stressor Pile-Up

Following terminology widely used in the literature on daily stress and affect, emotional reactivity to stressors refers to within-person stress-affect associations across repeated observations (e.g., Bolger & Schilling, 1991; Schilling & Diehl, 2014; Sliwinski et al., 2009). This study presents an approach to analyzing emotional reactivity to stressor pile-up that builds on the assumption that two aspects of stressor occurrence should be considered, that is, the number of stressors that have occurred within a given time interval and the time distances between stressor occurrences and the assessment of negative affective experiences. To illustrate, consider an experience sampling study with multiple assessments per day. It very likely makes a difference for a person’s level of negative affect if this person has experienced one or two stressors during a given time window. In the latter case, the rise in negative affect caused by the first stressor may not have fully ebbed away when the person experienced the second stressor (Wrzus et al., 2015). Thus, the person would have experienced greater negative affect during exposure to the second stressor than they would have if they had not also experienced the earlier stressor. Moreover, the additive effect of the two stressors arguably depends on the temporal spacing of the stressors. For example, if a second stressor occurred one hour later rather than three hours later, recovery from the first stressor would be less complete and the additive negative affect presumably would be higher in the one-hour scenario than in the three-hour scenario.

To the best of our knowledge, past work has not fully addressed this temporal spacing of stressors within short time windows as a predictor of emotional reactivity. To begin with, in a landmark study, Bolger et al. (1989) used daily reports over ten days to demonstrate that interpersonal stressors such as arguments with one’s spouse had stronger effects on emotional reactivity when these occurred repeatedly rather than once.

More recently, Grzywacz and Almeida (2008) used end-of-day reports to operationally define stressor pile-up on a given day as the number of stressors reported over the preceding three days. The authors showed that stressor pile-up over the three preceding days predicted binge-drinking (but not emotional reactivity) over and above same-day stressors. The analytic approach provided a straightforward quantitative operationalization of stressor pile-up that (a) was based on a sum score of stressor occurrences over a pre-specified time period preceding the daily measurements of the outcomes, (b) was varying over study days, and (c) allowed the estimation of effects on the outcome disentangled from those of the same-day stressors. Yet, the analytic approach did not allow drawing inferences about the role of the timing of stressor occurrences in that the more distant stressors (e.g., three days ago) were considered equally important as stressors that occurred closer (e.g., one day ago) to the outcome measurement.

Moving one step further, Schilling and Diehl (2014) made use of an analytic approach that allowed the impact of preceding stressors to decrease linearly over time by weighing their temporal distance to the outcome measurement. That is, the more days had passed since the stressor occurred, the lower the weight this stressor received to create the overall stressor pile-up score. Analyses revealed that a stressor pile-up index that utilized the information about the timing of stressor occurrence was indeed coupled with increased emotional reactivity over and above the effect of concurrent daily stressors. However, the analytic approach was limited because it did not allow drawing inferences about non-linear forms of (a) how and how fast the stressor effect attenuated over time and (b) individual differences therein.

Considering these limitations, the general assumption that the effects of stressors will attenuate over time does not necessarily imply an attenuation at constant rate, meaning that the effects decay linearly across time. Rather, the rate of such decay may itself be driven by the time passed and/or the amount of decay reached at a given point of the attenuation process. For example, the law of exponential decay has been applied successfully across many different disciplines to model empirical processes of decay over time (e.g., to describe forgetting curves: Averell & Heathcote, 2011). We consider such exponential decay a reasonable candidate to describe how stressor effects attenuate over time. The basic rationale of exponential decay is to consider a process as a quantity that decreases at a rate proportional to its current value. Thus, exponential decay of how a given stressor shapes people’s affect would mean that the effect decreases more rapidly immediately after the stressor occurs and then slowly fades out with increasing time distance. In addition, it appears reasonable to assume that people differ from one another in the rate of exponential decay, varying particularly in how fast the stressors’ effects attenuate over time In the present study, we focus on such inter-individual differences, but also intra-individual differences in such attenuation, depending on the stressors experienced, could possibly be considered.

Overall, conceptual views on emotional reactivity to stressor pile-up are closely linked with the methodological approaches used to analyze such reactivity. With the above conceptual considerations in mind, the goal of this study was to extend our previous methodological approach (Schilling & Diehl, 2014) in four important ways. First, we tested an exponential decay function for the weights of the time distances for the piled-up stressors and compared this function to alternative “candidate functions” (constant rate of decrease: linear decay; increasing/decreasing rate of decrease: quadratic decay). Second, rather than pre-specifying the parameters of the decay function, we directly and freely estimated these from the data at hand. Third, we explicitly modeled individual differences in the time-distance weights by estimating random (i.e., person-specific) parameters of the decay function. Fourth, given the availability of micro-longitudinal ambulatory assessment data, we moved from considering stressor pile-up over preceding days to examining stressor pile-up within a given day. This allows for a more fine-grained understanding of the effects of the temporal spacing of stressors within a day on individuals’ emotional reactivity to the stressors and the potential pile-up of stressors.

Emotional Reactivity to Stressor Pile-Up in Old and Very Old Age

Prominent theories of emotional aging suggest that the affective consequences of stressor pile-up change across the adult lifespan. According to Socioemotional Selectivity Theory (Carstensen, 2006), for example, individuals become more motivated to down-regulate their negative emotions as they perceive their remaining lifetime as increasingly more limited with advancing age. The Strengths and Vulnerability Integration model (SAVI, Charles, 2010) adds that older adults may not only be more motivated to down-regulate their negative emotions, but may also be more skilled at doing so (Carstensen et al., 2000; Diehl & Hay, 2011). As a consequence, the effects of stressor pile-up on emotional reactivity may be attenuated with increasing age. Notably, however, and as eloquently stated by Charles (2010), aging does not only come with gains but also losses and vulnerabilities, particularly in basic cognitive and physiological functioning, making at least some forms of emotion regulation increasingly more difficult. This idea would suggest that the effects of stressor pile-up on negative emotions should become larger in old age, particularly if one considers that very old age is characterized by an increasingly negative ratio of gains and losses in more and more domains of functioning (Baltes & Smith, 2003; Gerstorf et al., 2018; Kunzmann et al., 2019).

The empirical evidence for age differences in the effects of stressors on negative affect is, however, not entirely consistent (for reviews, Charles, 2010; Schilling & Diehl, 2015) and, at the same time, limited in aspects addressed in this study.

Thus, the question of whether and how strongly within-day stressor pile-up affects negative emotions in old age has remained largely unaddressed, and so has the question whether very old age comes with greater or lower vulnerability to stressor pile-up. The daily diary study conducted by Schilling and Diehl (2014) might be regarded as an exception providing tentative evidence on these questions. In this study, the effect of stressor pile-up across days on negative affect was weaker in older as compared to younger adults. This suggests that older adults may be particularly skilled at down-regulating negative emotions over longer time periods, considering stressor pile-up effects as persisting impact of past stressors on negative emotions (Charles, 2010, Hay & Diehl, 2011).

However, this evidence may not generalize to the present study for two reasons. First, stressor pile-up across study days in a daily diary study differs in timing from within-day stressor pile-up because much more time has passed between stressors when stressor pile-up is assessed across days as compared to stressor pile-up across the past several hours on a given day. Second, it is possible that age-related trends from young to old adulthood as found in the earlier study will not continue from young-old to very old age. In particular, these trends may change because the transition into very old age often comes with accumulating losses of resources needed for emotion regulation. These losses may possibly outweigh self-regulatory gains achieved during earlier parts of the adult lifespan. Second, taken together, our focus here is more on short-lived processes and we follow SAVI (Charles, 2010) in assuming that among young-old and very old individuals age-related strengths and vulnerabilities in down-regulating negative emotional reactions to stressors might add up to some essential reactivity to within-day stressor pile-up. Considering that vulnerabilities increase and accumulate from young-old to very old age, we also expected that reactivity to within-day stressor pile-up would be stronger in very old adults compared to young-old adults.

The Current Study

Our general objective was to analyze how within-day stressor pile-up impacts young-old and very old individuals’ negative emotions in response to these stressors. We extended past work in both methodological and empirical ways. Methodologically, we extended previous work (Schilling & Diehl, 2014) to present a novel approach to operationalizing and analyzing within-day stressor pile-up effects on affective outcomes. Empirically, we analyzed the effects of within-day stressor pile-up on negative affect in a sample of young-old and very old individuals, permitting the study of individual and age differences in emotional reactivity to daily stressor pile-up during a stage of the adult lifespan that has rarely been targeted in past work. Regarding these empirical analyses, we hypothesized that (a) the pile-up of stressors that occurred over the day before an actual assessment of negative affect would predict increases in negative affect over and above the occurrence of a stressor at the time of assessment, and (b) very old adults would show greater susceptibility to within-day stressor pile-up than young-old adults.

Methods

Sample and Procedures

The current project used data from 123 young-old (age range 66–69; born 1950–52; women 47%) and 47 very old adults (age-range 84–90; born 1930–32; women 60%) who participated in the EMIL (Emotional Reactivity and Emotion Regulation – A Multi-Timescale Approach Added to ILSE) study, a multi-component project consisting of a laboratory-based psychological testing session and a seven-day ambulatory assessment. All of the young-old and 32 of the very old adults were followed-up from the Interdisciplinary Longitudinal Study of Adult Development (ILSE), an ongoing multidisciplinary longitudinal study that consists of four waves of data collection in the German cities of Leipzig and Heidelberg, covering twenty years of observation (for detailed information about the parent sample, see Sattler et al., 2017). To increase statistical power, we recruited 15 additional very old participants from the community via newspaper ads. The current study only used ambulatory assessment data. For more details and materials on the complete study, see https://osf.io/nhzpw/.

Eligibility requirements of participation included: Being able to read large-sized print, to hear an alarm clock, having no neurodegenerative diseases or brain dysfunction (e.g., stroke), and a Mini-Mental State Examination score greater than 24. To examine the selectivity of the current sample vis-à-vis the larger ILSE parent ample, we used logistic regression analysis on the following measures from the most recent (i.e., fourth) wave of the ILSE study: physical health, cognitive performance, depressive symptoms, education, sex, and age group. Better cognitive performance was positively associated with the probability of staying in the study (standardized OR = 1. 984, p < .001; short-form Wechsler Adult Intelligence total score; Dahl, 1972). All other predictors had non-significant effects. When the logistic regression analyses were performed separately for the two age groups, cognitive performance was again the only significant predictor for the young-old, and this effect appeared even larger, though not significant in the very old group (OR_young-old = 1.861, p = .004; OR_{very old} = 3.168, p = .055). Finally, comparing the 15 additionally recruited very old adults with those followed-up from the ILSE, the former showed fewer depressive symptoms (Cohen’s d = .59, p < 0.05), but did not differ otherwise.

The EMIL project was approved by the ethics committees of the Faculty of Behavioral Studies, Heidelberg University, and the German Society for Psychology (DGPs) and participants provided informed consent.

For the ambulatory assessment, participants were provided with a large-display tablet with touch screen interface (iPad), saliva kits, and a heart rate monitor (physiological data obtained will not be used in this study). In an initial baseline session, participants were introduced to the handling of these devices. Next, a 7-day ambulatory assessment phase was started, including six assessments (hereafter referred to as beeps) per day. At waking and prompted by beeps at 10 a.m., 1 p.m., 4 p.m., 7 p.m., and 9 p.m. participants provided self-reports on stressful experiences and affect, which were analyzed in the current study. Depending on their daily schedule, participants were allowed to deviate by 30 minutes before and up to two hours after the exact beep times to fill out the tablet-administered questionnaires. This protocol has been successfully implemented in other studies (e.g., Windsor et al., 2020; Wrzus et al., 2013). Average response times were close to the prescheduled times (first to sixth beep at 7:10, 10:06, 13:09, 16:10, 19:07, 21:09, respectively),and mean time intervals (standard deviations in brackets) were 2.94 (1.18), 3.03 (0.48), 3.03 (0.51), 2.96 (0.52), 2.05 (0.47) hours between subsequent beeps 1 to 6, respectively. Overall, valid ambulatory assessment data for 1,165 days and 6,686 beeps were obtained. On average, young-old adults participated on 6.95 days (SD = 0.38) out of the seven days and responded to an average of 5.81 beeps (SD = 0.53) out of the six beeps per day. Very old adults’ average participation was 6.60 days (SD = 1.38) and 5.55 beeps (SD = 0.87) per day. This indicates that compliance in following the study protocol was very high in both age groups.

Measures

Stressor

At each beep, participants were asked for the occurrence (i.e., if at least one stressful situation was experienced since the preceding beep) and perceived severity (“How severe was the aforementioned problem for you?”) of the most severe stressor. Stressor severity was rated using a slider on a 0–100 scale (0 = “not at all”, 100 = “strongly”).

Time Since Stressor Exposure

Once a stressor occurred, participants were asked (a) whether the stressful situation was still ongoing at the beep and, if this situation was not ongoing, (b) to report the time since exposure to the stressor (“How long has the situation been concluded?”), with time being counted in five-minute intervals by scrolling through a drop-down list. This self-report served to compute for each beep times since exposure to all stressors that occurred at the given day before the beep. If the stressful situation was still ongoing, time since exposure was coded zero.

Negative Emotions

At each beep, participants were presented with 12 negative emotion adjectives (angry, sad, depressed, disappointed, nervous, jittery, upset, downhearted, troubled, worried, afraid, irritable), to be endorsed on a 0–100 scale (“How … do you feel right now?”; 0 = not at all to 100 = extremely). The adjectives were selected from validated item lists to assess affect (Watson & Clark, 1999; Kessler et al., 2002), and have been widely used with older participants. The mean score served as indicator of current negative affect. We checked for two-level (within- and between-person) reliability by computing coefficient ω (McNeish, 2018): ω_within = .90 and ω_between = .98. This indicated high reliability at both levels (for computational details, see Bolger & Laurenceau, 2013, p. 138).

Statistical Analyses

Our approach to analyzing within-day stressor pile-up effects on negative affect had two parts. First, we operationalized within-day stressor pile-up by defining a time-varying accumulating indicator of stressor pile-up that exerts its effect at each beep. Second, we included this pile-up indicator as a within-person predictor in a mixed (multilevel) regression that predicts current negative affect measured at the beeps. Both parts were incorporated into one statistical model that simultaneously estimates the operationalization and regression parameters (i.e., no stepwise analysis). This approach is explained separately in the following section for reasons of comprehensibility.

Operationalization of within-day stressor pile-up

Following the reasoning described above, stressor pile-up at a given point in time was operationalized by adding up a person’s stressors measured on the given day up to the respective point in time and weighting these measures with the temporal distance that had passed since the stressor occurred. Thus, stressors for which more time had passed since their occurrence contribute less to current pile-up index. In separate analyses, we applied this operationalization to both measures of stressor occurrence and stressor severity. To express this in formal terms, let P_tdi denote the index of the stressor pile-up and S_tdi the stressor measure (for participant i at beep t and study day d) – then:

$$P_{tdi}\hspace{0.17em}=\hspace{0.17em}\sum _{j=0}^{t-1}{w}_{\left(t–j\right)i}{S}_{\left(t-j\right)di},$$ (1)

where w_{(t – j)i} denotes the weights given to the stressors in summing them up for the pile-up index P_tdi (i.e., j denotes the lag to beep t, and $S_{\left(t-j\right)di}$ is the stressor at the jth beep before beep t) For illustration, consider stressor pile-up at the 4^th beep of a given day: According to Equation (1) this will be the weighted sum of the stressors measured up to that beep: $P_{4di\hspace{0.17em}}\hspace{0.17em}=\hspace{0.17em}{w}_{4i}\hspace{0.17em}=\hspace{0.17em}{S}_{4di\hspace{0.17em}}+w_{3i}\hspace{0.17em}{S}_{3di\hspace{0.17em}}+w_{2i}\hspace{0.17em}{S}_{2di\hspace{0.17em}}+w_{1i}\hspace{0.17em}{S}_{1di\hspace{0.17em}}$. Note that this notation implies person-specific weighting (subscript i for the weights), but no within-person change of the weighting across days (no subscript d for the weights).

To allow for the stressors’ decreasing impacts over time, the weights were assumed to follow an exponentially decreasing function of the time that has passed since exposure to the respective stressor and beep t. Thus, in formal terms, w_(t-j)i in Equation (1) may be written as

$$w_{\left(t–j\right)i}\hspace{0.17em}=e^{-{\alpha }_i{\text{Δ}}_{(t-j)i}},$$ (2)

where ${\text{Δ}}_{(t-j)i}$ denotes the time since exposure to $S_{(t–j)di}$ at beep t. Note that when ${\text{Δ}}_{(t-j)i}\hspace{0.17em}=0$, then no time has passed since exposure, which indicates that the stressor is currently occurring at the time of the beep and the weight would be at the maximum of 1. In contrast, when ${\text{Δ}}_{(t-j)i}$ increases towards infinity, the weights would approach 0. Of note is also the coefficient α_i included in Equation (2), which indicates a person-specific exponential decay of the weights given to stressors across the day. With its negative sign and α_i constrained to positive values, higher α_is translate into steeper decay, meaning a shorter persistence of stressor burden over time.

We also examined two additional decay functions (piecewise-linear and piecewise-quadratic) that allow for alternative forms of how the weights decay since time of exposure. In line with our expectation, results revealed that the exponential decay function indeed fit our data best (for details, see Supplement 1).

Mixed regression model of stressor pile-up effects

With the stressor pile-up index operationally defined by Equations 1 and 2, it was embedded as a within-person predictor of negative affect in two-level (within- and between-person) mixed regression models. That is, we did not analyze three-level models (beeps within days within persons), but excluded the day-level, which accounted for only a small share (8%) of the total negative affect variance and could therefore be ignored for the sake of model parsimony. The basic analysis model was:

$$Y_{tdi}\hspace{0.17em}={\beta }_{0i}\hspace{0.17em}+{\beta }_{1i}{P}_{tdi}\hspace{0.17em}+{\beta }_{2i}{\dot{S}}_{tdi}\hspace{0.17em}+{\beta }_{3i}(P_{tdi}\times {\dot{S}}_{tdi})\hspace{0.17em}+{\beta }_{4i}{\overline{S}}_i\hspace{0.17em}+{\beta }_{5i}{T}_{tdi}\hspace{0.17em}+{\epsilon }_{tdi}$$ (3)

where Y_tdi denotes the response variable (i.e., negative affect assessed for individual i at beep t at day d). The predictors are as follows: P_tdi denotes the stressor pile-up as defined by Equation (1), and ${\dot{S}}_{tdi}$ refers to a current stressor ongoing at beep t (with ${\dot{S}}_{tdi}\hspace{0.17em}=\hspace{0.17em}0\hspace{0.17em}if\hspace{0.17em}{\text{Δ}}_{(t-j)}>0$). ${\overline{S}}_i$ denotes the person mean of S_tdi, which was included to control for inter-individual differences in the overall level of stress experienced during the observation period. T_tdi, denotes the daytime at beep t, centered at noon, which was added to the model to control for potential affective trends unfolding over the day. Finally, ε_tdi is the model residual.

Note again that in Equation (3) the stressor pile-up P_tdi includes the decay function with one additional person-specific parameter α_i. Thus, substituting P_tdi for the respective terms from Equations (1) and (2) yields the complete expression of the model with all coefficients to be estimated:

$$\begin{gathered} Y_{tdi}={\beta }_{0i}\hspace{0.17em}+{\beta }_{1i}{\sum }_j\left(e^{-{\alpha }_i{\text{Δ}}_{(t-j)i}}{S}_{(t-j)di}\right)\hspace{0.17em}+{\beta }_{2i\hspace{0.17em}}{\dot{S}}_{tdi}\hspace{0.17em} \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\beta }_{31i}\left(\left({\sum }_j(e^{-{\alpha }_i{\text{Δ}}_{(t-j)i}}{S}_{(t-j)di}\right)\right)\times {\dot{S}}_{tdi})\hspace{0.17em}+{\beta }_4{\overline{S}}_i\hspace{0.17em}+\hspace{0.17em}{\beta }_5{T}_{tdi\hspace{0.17em}}+\hspace{0.17em}{\epsilon }_{tdi} \end{gathered}$$ (4)

Six parameters in Equation 4 represent two-level (within- and between-person) mixed model random effects: First, β_0i denotes the random intercept, which indicates the score of negative affect predicted for the condition when all predictors have a score of zero (i.e., no stressor pile-up, no current stressor, average person-mean S_tdi, at noontime). Second, β_1i denotes the random effect of reactivity to stressor pile-up across the day, given no ongoing stressor. Third, β_2i is the effect of a stressor ongoing at the time of negative affect assessment, given no previous stressor pile-up. Fourth, β_3i represents an interaction effect that can be interpreted as the degree to which previous stressor pile-up amplifies reactivity to an ongoing stressor. Fifth, β_5i denotes a linear time trend in the outcome across the day. Sixth, α_i, the person-specific exponential decay of the weights given to stressors, is included as random effect to be estimated along with the β’s in the mixed model computation. To estimate α_i as random parameter of in two-level mixed model, constraining it to positive values and meeting the assumptions about its random effect distribution, we proceeded as described in detail in Supplement 2. In addition to these random effects, β₄ denotes the fixed (between-person only) effect of the individuals’ overall levels of stress accounting for between-person differences in negative affect. In a subsequent step, we added age group (effect coded) as predictor, including cross-level age-group interactions with all within-person level predictors.

Model computation and statistical power

All mixed model analyses were performed with SAS PROC NLMIXED, using the first-order integral approximation and Newton-Raphson with line search optimization (SAS Institute Inc., 2015, p. 6517–6617 for computational details). For readers interested to run or modify this model, we provide a detailed description of the model computation, including annotated SAS code in Supplement 3. This implies full information maximum likelihood estimation with missing-at-random treatment of missing values (Schafer & Graham, 2002). An R² indicating the amount of within-person variance accounted for by the estimates was computed ad hoc as the reduction of residual variance compared to the random-intercept-only null model (Xu, 2003).

Given the sample size of our database, the statistical power for testing the model effects under interest might be of concern. However, power analysis for mixed model effects is complicated as most power formulas do not cover mixed regression effects and mixed model power computation is still a field in need for more methodological research (e.g., Arend & Schäfer, 2018). Results from simulation studies that explored the sample size requirements for sufficiently powered conventional linear mixed models provide some confidence that our data permits “powerful” testing of the within-person level effects ($N_{between-person}=170$, average $N_{within-person}=40$, see e.g., Arend & Schäfer, 2018, Scherbaum & Ferreter, 2009). However, whereas it also may be questioned whether these results generalize to our model including nonlinearly connected effects, more serious power concerns apply to testing the cross-level interactions with age group. In particular, considering the highly imbalanced design due to the relatively small number of very old ― as compared with young-old ―participants may compromise the power of testing age-group effects (Konstantopoulos, 2010). Therefore, we ran ad hoc power checks for the age-group effects given the current sample size, using Monte Carlo simulation to gain at least tentative evidence of potential power problems. For the detailed description of the procedure and results, see Supplement 4. The results suggested sufficient power to detect at least medium sized cross-level interaction effects of age-group with β_0i, β_1i and α_i – the latter indicating age-group differences in reactivity to stressor pile-up and in the rate of the exponential decay, key to our study aims. However, the simulation results also indicated that testing age-differences in β₂, and particularly β_3i might have suffered from lack of statistical power.

Results

Stressor Occurrence and Pile-up

Overall, across persons and beeps, participants reported 1,266 stressors, that is, they reported a stressor at 19% of all beeps. Among young-old adults, stressors occurred at 16% (801 stressors in total) of the beeps, whereas very old adults reported a stressful event at 28% of all beeps (465 in total). Only few participants (n = 11, 6%) did not report any stressor across the ambulatory assessments. However, only 364 of the stressful events reported were currently ongoing at the beep, hence a current stressor occurred at only 6% of all beeps, and 65 participants (38%) did not report any current stressor at all. To illustrate the temporal characteristics of stressor occurrence, Figure 1 shows the distribution of the stressors over the 24 hours of a day. As can be seen, stressors were reported to have occurred across the whole 24-hour period, but more often during the mid-morning until midday (about 9am to 1pm) and again in the evening hours (6pm to 8pm).

Figure 1.

Percentage of Stressors Reported by Time of Day, Separately for Young-Old and Very Old Participants

To illustrate the clustering of multiple stressors within days, more than one stressor was reported on 343 days (29% of person-days), one stressor on 323 days (29%), and no stressor on 486 days (42%). Of the 170 participants, 110 (65%) reported at least one day with more than one stressor (young-old: n = 72, 59%; very old: n = 38, 81%). Eleven (6%) respondents did not report any stressor and 49 (29%) did not report more than one stressor per study day. To check whether sparse reporting of stressors was due to negligent or unreliable responding to the beeps, we checked the responses to the emotion items for implausible patterns – in particular, frequent choosing of the endpoints (i.e. 0 or 100) of the slider presented in the assessments. We found some tendency of an increased rate of zero scores in the emotion items at days when no stressor or only one stressor was reported or among participants who did not report any stressor or did not report more than one stressor per day. However, implausible patterns were rarely found. Zero scores in all emotion items occurred altogether only at 7 (0.1%) beeps, and zero cases with score100 in all emotion items were observed. All plausibility checks (SAS outputs) can be viewed at https://osf.io/pmjh5/.

Table 1 presents descriptive statistics for the individual occurrence and self-rated severity of stressors, and negative affect, as well as the between- and within-person correlations between these basic study variables. Three points are noteworthy. First, consistent with findings from previous studies, the overall level of negative affect experienced in daily life was relatively low (M = 10.33 on a scale from 0 to 100). Second, nominal age group differences in the range of medium effect sizes were obtained in all four variables considered here, with very old adults consistently reporting nominally greater negative affect (Cohen’s d = 0.81), more stressors (d = 0.69), greater stressor severity (d = 0.58), and more stressors per day (d = 0.59) than young-old adults. Third, intercorrelations suggest that experiencing a greater number of stressors as well as more severe stressors were associated with greater negative affect.

Table 1.

Descriptive statistics for main study variables negative affect, stressor occurrence, stressor severity: Between-person means and standard deviations of within-person means, within- and between-person correlations

	Mean (SD)a			Correlationsb
	Young-Old (n =123)	Very old (n = 47)	All (N =170)	Neg. Affect	Stressor Occurr.	Stressor Severity
Negative Affect	7.62 (10.64)	17.43 (13.30)	10.33 (12.21)	-	.32	.36
Stressor Occurrencec	.17 (.15)	.30 (.22)	.20 (.18)	.54	-	.77
Stressor Severity	7.47 (9.57)	15.02 (15.12)	9.56 (11.82)	.67	.88	-
Average no. of Stressors Per Day	0.94 (0.80)	1.52 (1.14)	1.10 (0.94)	.38	.93	.77

Notes.

^aBetween-person statistics, i.e. means and standard deviation of the variables’ person-means.

^bBelow diagonal between-person correlations between person-means, above diagonal within-person correlations between person-mean-centered scores.

^cDummy-coded: 1 = stressor reported at beep, 0 = no stressor.

Stressor Pile-Up and Emotional Reactivity

Exponential pile-up model

Results from estimating the pile-up model with the exponential decay function (Eq. 4) are shown in Table 2, for both stressor severity and stressor occurrence separately used as stress indicator S_tdi. All fixed effects were statistically significant and the general pattern of results was the same for both stress indicators, despite differences in the absolute values due to the different stressor scale units (i.e., stressor severity was rescaled to units of a 10-point difference on the original 1–100 severity scale; stressor occurrence was dummy-coded with occurrence = 1). We conducted likelihood-ratio tests of the random (co-)variances. Note that we estimated free random covariances between all β-coefficients, but no random covariance with the exponential coefficient α_1i (as explained in Supplement 2). All random variances were significant for all random coefficients.

Table 2.

Mixed Model Results: Fixed Effects of Concurrent Daily Stressors and Within-Day Stressor Pile-Up on Negative Affect, Persisting Stressor Pile-Up Burden Estimated with an Exponential Decay Function

	Stressor severity			Stressor occurrence
	Estimate	SE	P	Estimate	SE	P
Fixed effects:
Exponential Coefficient α	0.395	0.139	0.005	0.491	0.165	0.003
Intercept β0	8.329	0.716	<.001	8.383	0.784	<.001
Stress Pile-up β1	0.906	0.158	<.001	4.388	0.709	<.001
Current Stressor β2	2.457	0.281	<.001	13.444	1.492	<.001
Current Stressor×Pile-up β3	0.336	0.101	0.001	17.156	3.841	<.001
Person-level Stress β4	0.525	0.067	<.001	25.868	4.473	<.001
Daytime β5	−0.227	0.030	<.001	−0.231	0.031	<.001
Random co/variances:
Var(α)	0.746	1.158	<.001 a	1.464	2.130	<.001a
Var(β0)	78.92	9.042	<.001b	96.803	11.066	<.001b
Var(β1)	1.418	0.293	<.001b	34.650	6.712	<.001b
Var(β2)	5.854	1.193	<.001b	221.52	38.923	<.001b
Var(β3)	0.409	0.194	<.001b	959.38	336.38	<.001b
Var(β5)	0.074	0.016	<.001b	0.085	0.018	<.001b
Cov(β0 β1)	0.521	1.066	1.000 a	6.535	5.977	0.317a
Cov(β0 β2)	−0.019	2.083	1.000 a	12.183	13.732	0.317 a
Cov(β1 β2)	1.042	0.466	0.025 a	40.634	12.032	<.001 a
Cov(β0 β3)	−0.966	0.782	0.046 a	−39.327	38.530	0.317 a
Cov(β1 β3)	0.060	0.152	1.000 a	0.751	21.219	1.000 a
Cov(β2 β3)	−0.789	0.361	0.014 a	−222.63	82.617	0.003 a
Cov(β0 β5)	−1.044	0.296	<.001 a	−0.896	0.344	0.008 a
Cov(β1 β5)	−0.034	0.051	1.000 a	−0.199	0.242	0.317 a
Cov(β2 β5)	−0.225	0.101	0.025 a	−1.893	0.618	0.002 a
Cov(β3 β5)	0.075	0.038	0.046 a	4.562	1.759	0.005 a
Var(Residual)	58.187	1.080	0.005	58.999	1.104	<.001
Model R 2	0.360			0.351
Pile-up R 2	0.142			0.140

Notes. For all estimates the gradient of the negative log-likelihood function was sufficiently small (< 0.00005) to indicate accurate estimates at convergence (SAS Institute Inc., 2015). The estimates for exponential coefficient α and Var(α) are functions of estimates of basic model parameters γ and Var(γ), with γ = −1.808 (SE = 0.098, P < .001) and Var(γ) = 1.756 (SE = 0.711) for severity, and γ = −1.690 (SE = 0.109, P < .001) and Var(γ) = 1.967 (SE = 0.688) for occurrence. R² computation: Reduction of within-person residual variance, compared with the random intercept only null model (Model R²) and with the model with β1 and β3 pile-up effects excluded (Pile-up R²).

^aP-values from likelihood-ratio (−2LL-differences, df = 1) test.

^bP-values from likelihood-ratio test for total random component (i.e., random variance and all 5 covariances including the component, df = 6).

The results showed a linear decrease in negative affect that unfolded typically across the day (e.g., stressor severity model β₅ = −0.227), and persons who were on average exposed to more stressors per day across the study period reported higher negative affect (e.g., for stressor severity, β₄ = 0.525). Most important for our research questions are four parameter estimates: First, a specific effect of stressor pile-up (stressor severity β₁ = 0.906), indicating that stressor pile-up increased negative affect at times when no current, ongoing stressor affects the individual. Second, stressor pile-up interacted with current stressor experience (e.g., stressor severity β₃ = 0.336), indicating a greater increase in negative affect in response to a current stressor when stressors had already piled-up before, as compared to a current stressor that was not preceded by previous stressors (β₂ = 2.457). Note, however, that sestimates of β₂ and β₃ are based on relatively few occurrences of stressors ongoing at a beep (i.e., current stressor unpreceded by previous stressors: 181 beeps, 3%; current stressor preceded by previous stressors: 183 beeps, 3%). Thus, despite the significance of this effect, there is some doubt whether these estimates would hold for larger numbers of current-stressor-observations. Third, the estimate of the fixed exponential coefficient (α = 0.394 for severity, α = 0.491 for occurrence) provided an estimate of how (on average across individuals) the weights of stressors decayed across the day. Figure 2 gives an illustration of this decay, showing that the curve did not approach the zero line quickly within only few―say, 1 to 3―hours, indicating no fast decay of stressor burden, hence persisting across several―up to about 8―hours of the day. Fourth, while Figure 2 shows the estimated average decay, this effect also revealed significant random variance (e.g., severity model $Var(\alpha )\hspace{0.17em}=\hspace{0.17em}0.746$), indicating substantial between-person differences in the speed of this decay.

Figure 2.

Exponential Decay of the Stressor Weights as Estimated From the Current Data for the Stressor Pile-Up Function

Empirical Bayes estimates of the pile-up values that were implied in the model estimation can be obtained in SAS PROC NLMIXED and might be used as information about the range and distribution of the pile-up scores: For stressor severity, the range of the pile-up values was 0–30.5, with a mean value of M_pile-up = 1.0 (SD_pile-up = 2.3). For stressor occurrence, pile-up ranged from 0–3.5 with a mean value of M_pile-up = 0.22 (SD_pile-up = 0.39). Of course, as there were many beeps without a stressor reported previously on the given day, the pile-up values were highly right-skewed, scoring zero at 61% (skewness = 4.1) for severity, and at 59% of the beeps (skewness = 2.39) for occurrence. Based on these values, Figure 3 shows the regression lines for pile-up predicting negative affect without a current stressor, and given a current stressor ongoing at the beep. For comparability of the severity vs. occurrence effects, the regression lines were plotted against pile-up scaled to units of the above-mentioned standard deviations. The current stressors’ sample mean (i.e., mean severity of all stressors ongoing at the beep, M = 5.86) was used to compute the regression line for the severity model with current stressor. Figure 3 illustrates that the main effects of the pile-up, given no current stressor occurring at the beep, do not differ markedly when pile-up is based on severity vs. occurrence. Notably, the increase in negative affect predicted under high scores of pile-up is about the same as predicted by an current stressor without any pile-up, whereas there is a pronounced amplification of emotional reactivity in acute stressful situations due to the pile-up of preceding stressors across the day.

Figure 3.

Predictive Effects of Within-Day Stressor Pile-Up on Negative Affect With and Without an Ongoing Acute Stressful Situation in Daily Life, Regression Lines Cover the Pile-Up Sample Ranges

Finally, we conducted an additional analysis to assess whether the exponential pile-up model provided an enhancement in explaining stressor-related variability of daily negative affect over the conventional stressor reactivity model that has often been used in the literature. Specifically, we estimated mixed models using the simple stressor report―whether a stressor had occurred since the last beep, without taking into account the time since occurrence and/or whether the stressful situation was still ongoing―as predictor of negative affect (again controlling for the daytime at the beep and the person-mean of stress). For stressor severity, this conventional reactivity model revealed an ad-hoc R² = .252 (BIC = 47,694), and for stressor occurrence R² = .206 (BIC = 48,094), indicating substantial R²-decreases of .108 and .145 compared to the pile-up models for severity and occurrence, respectively (see Table 2).

Emotional Reactivity to Stressor Pile-Up in Young-Old and Very old Adults

To examine differences between young-old and very old adults, we added age group as a between-person predictor of all within-person random effects to the exponential pile-up model (i.e., the main effect of age group and interactions of age group with coefficient α, stressor pile-up, current stressor, current stressor × pile-up, and daytime). Again, we performed this analysis twice, using stressor severity and stressor occurrence as stress indicator S_tdi, and the general pattern of results was the same for both stress indicators. As seen in Table 3, inconsistent with our prediction of age group differences in emotional reactivity to stressor pile-up, none of the respective cross-level interactions were statistically significant. Thus, in comparison to young-old participants, very old participants were similarly reactive to stressor pile-up, and also did not differ in reactivity to concurrent stressors. There was, however, a statistically significant difference in the exponential coefficient (e.g., for stressor severity, age-group×coefficient α = 0.168). The age-group difference in α indicated that the affective burden from preceding stressors persisted longer for young-old individuals: For the severity model, the age group specific coefficients were α_young-old = 0.310 and α_{very old} = 0.478; and for the occurrence model α_young-old = 0.436 and α_{very old} = 0.559 (see Figure 4 for illustration). Aside from that, age-group differences appeared only in the “non-stressor-related” level of negative affect, which was higher in very old adults, as compared to young-old adults.

Table 3.

Age-Group Differences in Within-Day Stressor Pile-Up Predicting Negative Affect

	Stressor severity			Stressor occurrence
	Estimate	SE	P	Estimate	SE	P
Fixed effects:
Coefficient α	0.353	0.101	<.001	0.468	0.172	0.007
Intercept β0	8.309	0.683	<.001	8.276	0.753	<.001
Stress Pile-up β2	1.008	0.165	<.001	4.317	0.754	<.001
Current Stressor β1	2.548	0.272	<.001	13.162	1.515	<.001
Current Stressor×Pile-up β3	0.243	0.087	0.006	15.960	3.703	<.001
Person-level Stress β4	0.476	0.065	<.001	20.210	4.489	<.001
Daytime β5	−0.229	0.030	<.001	−0.238	0.030	<.001
Age-group×Coefficient α	0.168	0.070	0.018	0.123	0.047	0.011
Age-group	5.887	1.575	<.001	7.342	1.768	<.001
Age-group×Pile-up	0.356	0.347	0.306	1.171	1.330	0.380
Age-group×Current Stressor	−0.160	0.572	0.780	1.117	3.045	0.714
Age-group×Current×Pile-up	−0.208	0.239	0.387	−4.273	7.813	0.585
Age-group×Daytime	−0.124	0.067	0.065	−0.128	0.069	0.065
Random co/variances:
Var(α)	0.300	0.408	<.001a	1.040	1.684	<.001a
Var(β0)	73.394	8.408	<.001b	88.830	10.194	<.001b
Var(β1)	1.571	0.339	<.001b	36.198	7.056	<.001b
Var(β2)	5.668	1.140	<.001b	215.08	37.990	<.001b
Var(β3)	0.318	0.150	<.001b	961.20	344.29	<.001b
Var(β5)	0.073	0.016	<.001b	0.075	0.017	<.001b
Cov(β0 β1)	0.792	1.089	0.317a	10.634	6.040	0.083a
Cov(β0 β2)	−0.229	1.962	0.157a	11.383	13.082	0.317a
Cov(β0 β3)	−0.736	0.681	0.046a	−23.216	38.063	1.000a
Cov(β0 β5)	−0.882	0.277	<.001a	−0.758	0.316	0.014a
Cov(β1 β2)	1.065	0.475	0.025a	41.208	12.861	<.001a
Cov(β1 β3)	−0.062	0.159	1.000a	−19.201	33.001	1.000a
Cov(β1 β5)	−0.037	0.054	1.000a	−0.291	0.251	0.317a
Cov(β2 β3)	−0.881	0.349	0.003a	−240.40	83.781	0.002a
Cov(β2 β5)	−0.200	0.096	0.046a	−1.728	0.601	0.003a
Cov(β3 β5)	0.078	0.035	0.046a	4.603	1.772	0.005a
Variance(Residual)	58.427	1.086	<.001	59.180	1.113	0.005
Model R 2	0.358			0.349

Notes. For all estimates the gradient of the negative log-likelihood function was sufficiently small (< 0.0003) to indicate accurate estimates at convergence (SAS Institute Inc., 2015). Age-group effect-coded. Model R² computation: Reduction of within-person residual variance, compared with the random intercept only null model.

^aP values for random co-/variances obtained from likelihood-ratio (−2LL-differences) tests.

^bLikelihood-ratio test for total random component, i.e. random variance and all 5 covariances including the component.

Figure 4.

Age Group Specific Exponential Decay of the Stressor Weights as Estimated From the Current Data for the Stressor Pile-Up Function

Given the insignificant age-group effects and the small sample size of the very old sub-sample, these tests might have suffered from insufficient power. We performed ad hoc power checks for the age-group effects as mentioned in the Method section and described in detail in Supplement 4. The results suggested with regard to our key interest in the effect of stressor pile-up, that we did not miss a medium or larger age-group difference in this effect because our test lacked power. However, this might be the case with the age-group effects on the reactivity to a current stressor and on the current stressor × pile-up interaction, as these tests seemed critically underpowered.

Discussion

Although stress researchers have been aware for a long time that the effects of single stressors in everyday life can pile up (Bolger et al., 1989; Fuller et al., 2003; Grzywacz & Almeida, 2008), investigating and modeling the process of stressor pile-up has been a fairly recent enterprise. The few previous approaches have addressed stressor pile-up across―but not within―days and rarely took into account the temporal distance of stressors that piled-up before the affective outcome was assessed. We propose a concept of reactivity to within-day stressor pile-up that rests upon the idea that the temporal distance among stressors is critical, with stressors become more burdening with smaller temporal distance.

Effects of Stressor Pile-Up on Emotional Reactivity

Our findings corroborate the general expectation that the pile-up of stressors that occurred over the day would predict increases in negative affect. It did so over and above the effects of a current stressor co-occurring at the time of assessment, accounting uniquely for about 14% of the within-person variance in negative affect. Notably, the intra-individual R²s obtained with the pile-up model also outperformed those from a conventional negative affect reactivity model that has been used in many studies, analyzing within-person associations between negative affect and simultaneously assessed stress measures. Thus, taking into account the changing load of stressor burden provided by preceding stressful experiences contributes to a more comprehensive understanding of negative affect reactivity.

In particular, two findings put some finer grain into the picture, namely the pile-up and the exponential coefficient of the decay function of stressor weights that both exhibited significant fixed effects and significant random variances. First, stressor pile-up was related with negative affect (significant fixed effect) and individuals differed in how much such pile-up provoked negative affective reactions in their daily lives (significant random effect variance). Second, stressor “pile-up” was not the same across individuals: The fixed estimate of the exponential coefficient indicated that the affective burden of stressors that occurred across the day generally decayed as time passed, but the significant random variance of this parameter revealed that individuals differed in the rate of this decay. Taken together, these results suggest that an individual’s affective reactivity to within-day stressor pile-up might be driven by two aspects: (1) their typical intensity of negative affect reactive to stressors that have piled-up across the day; and (2) their typical rate of “getting over” or distancing from stressful experiences. One exciting direction for future research is to investigate these two aspects as unique facets of resilience to daily stressors and/or other kinds of negative events.

Aside from the focus on the stressor pile-up effects, other results of our study deserve attention. Although it was not surprising that an ongoing stressor predicted a substantial increase in momentary negative affect, this increase appeared further boosted by pile-up from previous stressors up to the time of the assessment. The respective interaction effect might be interpreted in terms of increased affective vulnerability in stressful situations, because the person has to deal with more stressors that occurred before that situation. However, it should be kept in mind that the occurrence of a current stressor during an assessment was a rare event in our study, so it may be asked whether the effects involving the current stressor would hold for a more “representative” sample of negative affect assessments within stressful situations. Moreover, de-trending the negative affect measures across daytime, we also found a significant general tendency of (linear) decline of negative affect across the days, unrelated to the occurrence of stressors. We refrain from speculative interpretations of this finding, as this goes beyond the scope of the current study; however, this finding might warrant further investigation in independent studies.

Emotional Reactivity to Stressor Pile-Up in Young-Old and Very old Adults

In contrast to our expectation, very old adults did not show more susceptibility to within-day stressor pile-up than young-old adults. That is, the very old adults appeared neither more nor less reactive to stressor pile-up. They also did not differ in reactivity to an ongoing stressor; and their reactivity to an ongoing acute stressor was neither more nor less affected by stressor pile-up. However, a difference between the age-groups was found for the exponential coefficient, indicating that the very old tended to distance themselves faster from stressful experiences than the young-old. Notably, Scott et al. (2017) reported a similar effect of continuous age (ranging from 25–60). They found that increasing time distance to a stressor (reported at a beep) predicted less “reactive” increase in negative affect, and this effect was amplified by increasing age.

Explanations for this finding are, at his time, speculative and tentative. It could be that a lifespan gain in emotion-regulatory competence, as documented in the literature (Charles, 2010; Schilling & Diehl, 2015), persists even after people have moved into very old age and such an advantage may manifest in the rate of down-regulating stressor reactivity rather than in limiting the magnitude of emotional reactions. That is, very old adults might experience more stressors which they already―and more often―experienced before in their lives (Brose et al., 2013; Schulz, 1985), making it easier to cope with these stressors quickly and stop worrying about them. This could provide an adaptive benefit compared to younger persons, though not in terms of an attenuated reaction to a given load of piled-up stressor burden, but in that timely distant stressors contribute less to that load.

Methodological Challenges Modeling Stressor Pile-Up and Emotional Reactivity

Analytically, our operationalization of affective reactivity to within-day stressor pile-up was driven by the assumption that a fine-grained analysis of pile-up effects required us to consider that individuals not only differ in the magnitude of emotional reactions to stressor pile-up, but also in how time works for them in getting over negative emotions provoked by the stressors. Thus, one key feature of the pile-up model presented in this study is the modeling of the time-distance-related exponential decay of stressor weights as a random parameter, freed to vary inter-individually.

The price paid for these novel modeling features is an increase in model complexity, compared to previous pile-up modeling approaches (e.g., Grzywacz & Almeida, 2008; Schilling & Diehl, 2014). Thus, the finding that this model worked successfully, delivering converging optimizations with accurate parameter estimates, can be taken as an important result on its own. It suggests that this modeling approach is suited and promising for further in-depth analyses of stressor pile-up effects in the context of micro-longitudinal studies with several assessments per day. Generally, the approach demonstrated here―in particular the key features mentioned above― adds to the statistical toolbox for analyses of processes of within-day reactivity to daily events.

In this context, the present pile-up model should be compared with two other recent proposals to examine affective within-day processes in response to multiple stressors within the day, taking into account the timing of these. First, Scott et al. (2017), although not directly addressing the issue in terms of pile-up of stressors, aimed for a process-oriented view of stressor-driven momentary affect including time since event as key variable to distinguish periods within this process. The authors stated that “naturalistic stress studies do not always provide clear demarcation between pre-stress, stressor event, and recovery periods. This has created both ambiguity and inconsistency in the use of a key concept in daily stress research, namely stress reactivity” (Scott et al., 2017, p. 178). The authors’ statistical modeling shows some fundamental similarity to the pile-up model proposed in the present study, in that both models imply a lagged-regression of momentary negative affect on the stressors that pre-occurred within the day. Conceptually, both models differ in their focus on a demarcation of periods in the daily stress-processes versus on the load of affective stressor burden, resulting from the continuous run of such processes. If multiple stressors occur within a day, periods of reactivity and recovery, as distinguished by Scott et al. (2017), may overlap and may not be easily demarcated. In this regard, the pile-up model may be a strategy to circumvent the problems of applying such clear-cut demarcations. In addition, the parametrization of the pile-up model might also hold some meaning with respect to the above mentioned demarcation. In particular, the model’s exponential coefficient, indicating the rate of the decay of a stressor’s impact on the affective outcome might be seen as an indicator of stressor recovery, following the terms of Scott et al. (2017).

Second, Smyth et al. (2018) used the term “pile-up” to refer to whole stress processes clustered in time, which led them to a broadly defined concept of pile-up. The authors stated: “Our view is that, broadly speaking, pile up reflects the frequency with which one is pulled out of homeostatic range of functioning” (Smyth et al. 2018, p. 22). Obviously, this conceptual view differs from those of earlier studies in that it encompasses the pile-up of entire stress processes (occurrence of, reactivity to, and recovery from stressors) rather than pile-up of stressor occurrences only. Considering that the pile-up of stressors within days implies multiple stressor reactive processes, hence also “piled-up” affective reactions and recoveries from these reactions, the proposal by Smyth and colleagues provides a more generalized framework to describe and understand daily processes of affective changes driven by stress. The theoretical breadth of this concept prevents a singular complete empirical operationalization that would include all its components. Rather, empirical research might address specific aspects of this pile-up concept (e.g., see a first operationalization by Almeida et al., 2020). It might, however, be difficult disentangle the share of changes due to recovery vs. reactivity that contributed to an affective score at a given point in time, in particular considering that individuals likely may not recover completely prior to encountering the next stressor. Again, estimating the load of affective stressor burden at a given point in time resulting from continuous and overlapping processes of reactivity to and recovery from stressors as implemented in our study might serve to circumvent such difficulties, distinguishing at least reactivity to a current stressor from stress-related changes due to previous stress experiences.

Study Limitations

We note several limitations of our study. First, it may well be possible that reactivity to stressors varies within a given person from stressor to stressor, that is, one size of reactive negative affect increase may not fit all stressful experiences (e.g., Smyth et al., 2018). One way to address this limitation, as has been applied in several studies of reactivity (e.g., Hay & Diehl, 2010; Koffer et al., 2016), might be to distinguish different types of stressors and estimate differential reactivity to these. However, also distinction of stressor types provides only a partial solution to this limitation because varying reactivity to stressors should not be restricted to different types but could be due to multiple idiosyncratic conditions of a stressful situation. In that regard, however, we considered it crucial to not only include stressor occurrence as a stress indicator, but also the stressor severity ratings, which presumably reflect to some extent intra-individual differences in how individuals are emotionally affected by different stressors.

Second, as Smyth and colleagues (2018) noted, most analytical approaches for analyzing components of the stress response focus on between-person differences but neglect the possibility that individuals may fluctuate in their stress response and recovery within themselves across time and contexts. This observation also applies to the current study. Reactivity to stressor pile-up and to acute stressors, as well as the rate of the decay of stressor weights over time may change intra-individually, from day to day or even within days. Extending the current modeling approach to estimate such intra-individual change is limited by the data at hand. To estimate variability of reactivity within days, many more than six assessments per day would be needed. Also, given ambulatory assessments across several days, running three-level mixed models with between-day variation in the first level random coefficients might appear another choice, providing estimates of intra-individual day-to-day variation of the crucial parameters. Our decision for a two-level model neglecting the between-day level was based on reasons of model parsimony in lieu of applying a non-linear mixed model that requires for model convergence many data points at each level. A rather small share of day-to-day variance in the total variance of negative affect in our view justified the two-level model; thus, neglecting potential day-to-day variation in the reactivity and the exponential decay parameter should not bias the fixed effect estimates of the effects, which were key to our study aims.

Third, the validity of the stressor severity ratings may be questioned. Did these ratings indeed measure the intensity of the stressor at the moment of occurrence? Or did they reflect the individual’s progress in coping with the stressor, rating it more or less stressful in hindsight? Regrettably, this question cannot be resolved with the data at hand, but it is reassuring that the results showed no marked differences in the analyses of stressor severity when compared with stressor occurrence.

Fourth, the reporting of stressors might have been to some extent incomplete because participants were asked at each beep to report the occurrence and severity of one stressor. If multiple stressors occurred since the last beep, participants were instructed to report on the one they perceived as most severe. This procedure was chosen to keep the assessments short and prevent disruption of the respondents’ everyday routines by the beeps itself. Obviously, if multiple stressful events had co-occurred frequently from one beep to the next, this would have changed the estimates of stressor pile-up. At the same time, the overall number of daily stressors reported in this study, which was consistent with other studies on older adults (e.g., Brose et al., 2013; Schilling & Diehl, 2014), suggest that the daily lives of older adults are typically not characterized by so many stressful events that these might succeed each other in extremely short time intervals.

Finally, the small sample size of the very old subsample is another limitation, particularly with regard to the age group comparisons. Power checks indicated that at least the age-group differences in reactivity to the current stressor and the current stressor × pile-up interaction could not be tested for significance with sufficient power. For the other age-group comparisons there might have been sufficient power to detect medium, but not small effects. Thus, non-significant age group differences could simply be due to insufficient statistical power of testing. This problem typically plagues studies with very old adults. Specifically, this age group in the ILSE parent sample was affected by high attrition due to death and poor health. Also, those still reachable in their late 80s at the time of the ambulatory assessments were not easy to recruit for seven consecutive days of assessments with multiple beeps per day and requiring them to use a technical device that most of them were unfamiliar with.

Therefore, and finally, although we did not find strong selection effects in comparison to the ILSE parent sample, a survivor effect cannot be ruled out, in that those who could manage the testing schedule were overall fairly healthy and motivated. Consequently, our findings may not necessarily generalize to less positively selected segments of the very old adult population.

Conclusion and Outlook

For the study of emotional reactivity to daily stressful events, the persistent effects of multiple stressors across the day account for a critical share of such reactivity, over and above the immediate rise in negative emotions associated with the co-occurrence of a single stressful event. The stressor pile-up model presented in this study provides a viable method to analyze these effects, hence adding to a nuanced, fine-grained picture of how everyday stressors may affect the daily affective well-being of older adults. In particular, our findings suggest that negative affect associated with stressors piled-up within a day decays on average non-linearly over time, following a pattern that may be well fitted by exponential decay curves that vary between persons in the rate of the decay. Furthermore, the current approach and our findings hold promise to further researchers’ understanding of age-related differences in daily stress processes. To this end, not only age per se―indexing the time individuals had to habituate to and “practice” coping with daily stressors―might shape reactivity to and/or the speed of recovery from previously piled-up stressors, but also social and physical conditions that change in later life denote promising predictors for future study.