Trait Social Anxiety Moderates the Relationship Between Emotion-Regulation Strategy Switching and State Anxiety in Daily Life

Abstract

Difficulty knowing when to switch emotion regulation (ER) strategies is theorized to be a key pathway to emotion dysregulation, but relatively few studies have empirically examined this. We applied a new order-based metric to quantify how N=109 socially anxious people switched between 19 different ER strategies (or chose not to regulate at all) throughout a 5-week ecological momentary assessment study yielding 12,616 observations. We tested whether state and trait anxiety reports, and their interaction, predicted differences in ER strategy switching. Results indicated that people with relatively higher social anxiety symptoms switch more often between ER strategies during periods of high average state anxiety but less often during periods of high variability in state anxiety than less socially anxious people. Interventions focused on helping socially anxious people learn how ER strategies are connected to variations in state anxiety might hold promise to increase adaptive ER switching decisions. More broadly, expanding ER switching interventions to consider the role of changing situations is an important next step.

Prominent theories of emotion regulation (ER) note that how an individual switches between their ER strategies from one moment to the next predicts well-being (Aldao et al., 2015; Bonanno & Burton, 2013; Gross, 2015; Southward et al., 2018; Webb et al., 2012) and problems effectively switching between strategies may lead to emotion dysregulation (Gross, 2015). From one perspective, repeatedly changing strategies before any positive effect could realistically be gained from any one strategy might indicate a flailing or impulsive pattern of ER (Southward et al., 2021). From another perspective, failure to change strategies in response to clear strategy shortcomings or relevant contextual changes might indicate an overly rigid pattern of ER (Bonanno & Burton, 2013). Switching between ER strategies too much or too little, then, may indicate that adaptive ER choices are not being made from one moment to the next.

Despite theoretical emphasis on problems with switching between ER strategies, relatively few studies have empirically examined the order of changes in ER strategy choices from one moment to the next (see Birk & Bonanno, 2016; Daniel et al., 2022; Eldesouky & English, 2022; McKone et al., 2022; Southward et al., 2018 for the small number of papers that have looked directly at ER switching). Instead, it has been more common to use variability-based metrics (that look at extent of variation in choices overall but do not consider the order of those changes) to infer switching. Variability-based studies do, however, still bolster the argument that some degree of switching between strategies across time is emotionally adaptive. For example, across four experience sampling studies, variably choosing between different ER strategies within a given situation in daily life was associated with reduced negative affect (Blanke et al., 2019). People with major depressive disorder reported lower trait ER diversity—a newer metric, which measures the variety, frequency, and evenness of the ER strategies that a person uses but not the order in which those strategies are used—across putatively adaptive ER strategies than people without a history of depression (Wen et al., 2021). Further, well-being was highest for individuals whose strategy use was best described by multiple combinations of active ER strategies over a three-week study in daily life, suggesting high rates of ER switching in people with more positive mental health attributes (Grommisch et al., 2019). That said, other findings suggest that more frequent ER switching during a given stressor (Southward et al., 2018) and greater ER diversity when using putatively maladaptive ER strategies (Wen et al., 2021) are associated with more adverse mental health attributes.

Taken together, theory and empirical findings suggest that ER strategy switching can either appear adaptive or maladaptive. Additional investigations—especially those that leverage time-ordered information within people’s ER choices—may help clarify under what conditions ER strategy switching is or is not associated with better mental health. The current study will apply a new, order-based analytic technique to investigate how people with elevated social anxiety symptoms switch between ER strategies within their everyday lives. We focus on the general level of instability in strategy selections made over time (i.e., how often some type of switch was made) rather than any specific type of switch (i.e., how often a switch from cognitive reappraisal to distraction was made versus a switch from distraction to cognitive reappraisal).

Sequence in ER Strategy Choice

Common approaches to analyzing daily life ER data focus on the relative frequency or likelihood for a person to use certain strategies over others depending on trait-level characteristics (e.g., emotion control values: Goodman et al., 2021; emotion malleability beliefs: Daniel et al., 2020) or changing contextual features (e.g., social setting: Daros et al., 2019). While informative, these investigations do not make full use of the time-based order of observations inherent in daily life data; they essentially examine averages or other order-agnostic summary statistics (e.g., variability) of reported ER use.

To illustrate the utility of considering sequenced (i.e., order-based) data, take for example two different patterns in how a person could use expressive suppression and emotion expression while navigating different stressors throughout their daily life. In one case, a person could repeatedly suppress their emotions across many different contexts and stressors until reaching a point, halfway through the study monitoring period, where they can no longer hold their emotions in, and so they resort to excessive, repetitive emotion expression (even in situations where expressing their emotions is not strategic, like when meeting new work colleagues). In a second case, a person could switch back and forth between emotion suppression and expressive suppression across the study monitoring period—perhaps in line with changing circumstances and stressors—in such a way that allows them to acknowledge their emotions without blowing up. If strategy use was sampled regularly, both patterns would be indistinguishable from one another using static, frequency-based analytic approaches (e.g., mean, standard deviation, variance) even though they are markedly different from a dynamic, sequenced perspective. Thus, we can gain a deeper understanding of emotion (dys)regulation by examining the sequence of ER choices in daily life.

Problems with ER Strategy Switching in Social Anxiety Disorder

Socially anxious people tend to overly rely on avoidance-oriented strategies in the relative absence of many other ER strategies (Khakpoor et al., 2019). As such, socially anxious people have been described as inflexible and rigid regulators (Goodman & Kashdan, 2021; Kashdan et al., 2011). This might suggest that socially anxious people switch less often between ER strategies than their healthy counterparts. However, our recent work in a clinical analogue sample of adults with elevated trait social anxiety¹ found that social anxiety severity was higher in participants who demonstrated greater ER diversity throughout daily life. This finding held after covarying the intensity of participants’ average state anxiety throughout the study (Daniel, Larrazabal, et al., 2023). If replicated, this unexpected finding might indicate that socially anxious individuals feel a heightened sense of urgency to reduce their anxious distress as quickly as possible, which drives their deployment of many different ER strategies. This might suggest that socially anxious people switch more often between ER strategies than their healthy counterparts. Given these competing possibilities, social anxiety presents an interesting opportunity to investigate the relationship between ER switching and psychopathology.

Specifically, we will apply a recently developed analytic technique (called ‘stability’, Daniel et al., 2022) to five weeks of daily life data from a sample of adults with relatively high trait social anxiety severity to test whether between-person differences in trait social anxiety severity or in state anxiety predict ER strategy switching patterns observed in daily life. Stability measures the extent to which a person repeats the same strategy between back-to-back surveys versus switches between strategies across surveys over a specified number of survey responses (details about stability’s calculation are provided in the methods section below). Our investigation focuses on ER strategy switching between randomly timed surveys often collected hours apart that are not necessarily linked to the same stressor. So, we conceptualize switches as changes in strategy that likely occur across different stressors (e.g., ruminating in response to a misunderstanding with a friend and then later practicing acceptance in response to strong physical sensations of anxiety) rather than throughout the regulation of a single stressor (e.g., ruminating about a speech gone wrong before practicing acceptance with respect to that same speech).

ER Strategy Switching and State Emotion Intensity

While many dynamic factors in daily life likely interact to influence ER switching decisions (e.g., emotion goals: Tamir et al., 2013; regulatory self-efficacy: Daniel et al., 2020; actual skill for using each strategy: Southward & Cheavens, 2020; contextual demands and opportunities: Rottweiler et al., 2018; perceived situational control: McKone et al., 2022), the current study examines the direct association between changes in state anxiety intensity and ER switching patterns. We focus on anxiety intensity because, according to Gross’s (2015) extended process model of ER, perceiving a strong emotion activates a goal to regulate, which in turn leads to strategy selection and implementation. Further, how intense the emotional experience is predicts not only whether a person will regulate, but it also predicts how they will regulate. For example, people tend to choose distraction over reappraisal when responding to highly intense negative stimuli (Sheppes et al., 2014), a pattern that appears to be more effective and less effortful than trying to reappraise intensely negative situations (Shafir et al., 2015). However, choosing reappraisal over distraction when emotional intensity is less extreme has also been linked to adaptive ER (Birk & Bonanno, 2016). Beyond driving different strategy selection decisions, differential changes in emotional intensity are also likely explained by different strategy selection and implementation (e.g., Daniel et al., 2019). As such, we suspect the relationship between changing anxiety intensity and ER switching decisions is likely bidirectional.

We highlight three distinct features of a person’s anxiety intensity that may be associated with ER switching over time. We illustrate each potential relationship from both causal directions (i.e., ER switching influencing anxiety intensity and vice versa), although we acknowledge that the association could also be explained by a third variable (e.g., changes in social context). First, how intense their anxiety has been, on average: A period of intense average anxiety might spur many different regulation attempts to resolve the anxiety, while a period of low average anxiety may not motivate the use of many different strategies. Alternatively, a period of relatively higher ER switching might be inherently destabilizing to a person’s emotional experience and leave anxiety levels high. Second, whether their anxiety has been increasing or decreasing in intensity: Increasing anxiety intensity might signal that a change in strategy is needed whereas decreasing anxiety intensity might signal that an effective strategy has been found. Alternatively, repeatedly using a given strategy could yield incrementally fewer anxiety reduction benefits over time until no more progress is possible with that strategy. Third, how variable their anxiety intensity has been: Very different levels of anxiety intensity might prompt the use of very different strategies because some strategies are better suited to intense anxiety whereas others are better suited to low levels of anxiety. At the same time, switching between strategies that typically reduce anxiety to different degrees will likely lead to more variable anxiety reports.

Responsiveness to State Anxiety in Social Anxiety Disorder

People differ in how much they match their ER choices with differing levels of emotional intensity (Füstös et al., 2013). Socially anxious people may evidence a different relationship between their state anxiety and ER strategy switching decisions because they are especially sensitive to anxiety and are typically less willing to endure their anxious distress than non-socially anxious people (Khakpoor et al., 2019). This low distress tolerance may lead socially anxious people to make rigid attempts to avoid or escape their anxiety as quickly as possible through strategies like situation selection, experiential avoidance, and expressive suppression (see Kashdan et al., 2013). Alternatively, low distress tolerance may lead socially anxious people to use more ER strategies than healthy control participants in response to stressful events (Goodman et al., 2021) as they flail between strategies to find rapid relief from their negative affect. As such, it is especially interesting to investigate the extent to which trait social anxiety symptom level moderates the association between state anxiety intensity and ER switching patterns.

Overview and Hypotheses

This study will examine how trait and state anxiety relate to ER strategy switching patterns throughout the daily lives of N = 114 socially anxious adults. Participants were instructed to submit up to six randomly timed surveys per day asking them to report their state anxiety intensity and how they were regulating their emotions from a list of 19 strategies. Participants could also report that they were not regulating their emotions at the time of the survey.² We repeatedly calculated the degree of stability (our measure of switching) in each participant’s ER choices at different points throughout the 5-week study—where higher stability values reflect a tendency to repeatedly use the same strategy from one survey to the next (lower rates of switching), and lower levels of strategy stability reflect a tendency to rarely report using the same strategy between adjacent surveys (higher rates of switching). We also characterized what each participant’s state anxiety was like during each window that contributed to a given ER stability value using the following metrics: mean level of anxiety (i.e., average level of anxiety intensity across ratings), first derivative in anxiety (i.e., rate of change in anxiety across ratings), standard deviation in anxiety (i.e., degree of variability in anxiety across ratings). We chose these metrics because they each capture distinct features of a person’s short-term affective experience that seem likely to be associated with ER switching decisions in the ways illustrated above. We tested whether trait social anxiety symptom severity or any of the state anxiety descriptive measures (mean, first derivative, standard deviation) predict different levels of ER stability. Finally, we tested whether trait social anxiety severity moderates the relationship between the state anxiety descriptive measures and ER stability. The following hypotheses were all preregistered.

Between-person, we expect that, on average, participants with higher levels of trait social anxiety symptom severity will have more stability (lower rates of switching) in their ER strategy choices than participants with lower trait symptom levels. Our hypothesis is based on findings that socially anxious people tend to rigidly over-rely on avoidance-oriented strategies (Aldao et al., 2014; Goodman & Kashdan, 2021; Kashdan et al., 2011) and the more rigid an ER profile is, the more stable it will be. However, we acknowledge that it is also possible participants with higher trait social anxiety will have relatively less stability (higher rates of switching) in their ER strategy choices, in part because socially anxious people tend to experience more extreme levels of negative affect that instigate repeated regulatory responses (Cohen et al., 2017) and their initial ER strategy implementation is less likely to be fully effective, prompting a search for an alternate strategy to reduce the residual distress. In support of this plausible alternative hypothesis, people with social anxiety disorder have been found to use a greater number of regulatory strategies per stressful event than healthy control participants (Goodman et al., 2021) and using more strategies probabilistically decreases expected stability values (Daniel et al., 2022).

Within person, we expect that ER stability will be higher (lower rates of switching) when the average of all state anxiety ratings during that period of time is lower, is less variable, and when the rate of change is less negative. This would suggest that people do not shift their strategies when their state anxiety is relatively less intense, is not shifting around as much, and tends to be changing towards a less anxious state over time, respectively; put simply, people are less likely to stop what they are doing and switch to something else if they are feeling relatively good or their current approach seems to be working for them (Bonanno & Burton, 2013; Carver, 2015). Importantly, while theory emphasizes the role of affect monitoring to inform strategy choice, we measured state anxiety and ER concurrently. As such, it is also very plausible that ER switching influences how anxiety fluctuates over time or that they are associated but neither drives the other. For example, while not the focus of the current study, it is important to keep in mind that situational changes in a third variable, such as location, type of stressor, or social context, could drive both ER strategy deployment and level of anxiety. In practice, we suspect the influence between ER strategy deployment and anxiety is bidirectional, but we build our predictions for the current paper from the theories which emphasize how state anxiety influences strategy switching decisions (because our design is not well suited to tease apart the distinct bidirectional influences and given a stronger theoretical basis for this direction, see Bonanno & Burton, 2013).

Finally, we expect that trait anxiety will moderate the relationship between state anxiety and ER stability such that state anxiety and ER stability will be more strongly associated in individuals with higher versus lower trait levels of social anxiety symptoms. We expect these cross-level interactions because people with higher (vs. lower) levels of social anxiety are especially sensitive to anxiety and less willing to tolerate distress (Khakpoor et al., 2019), so they may be overreactive to changes in state anxiety when deciding how to regulate and update their ER strategy choices.

Transparency and Openness

All hypotheses and plans for analyses for this secondary data analysis were pre-registered on the Open Science Framework (OSF; https://osf.io/yfvbr). Analysis scripts are available on OSF at https://osf.io/3urej and all data are available at https://osf.io/xadyp. We report how we determined our sample size, all data exclusions, all manipulations, and all measures in the study. Given this is a secondary data analysis for which we did not conduct a priori power analyses, all non-significant results should be interpreted with caution. All participants provided written informed consent to participate in this Institutional Review Boards-approved study (University of Virginia IRB #2018-0018-00).

Method

Participants

One hundred and fourteen individuals who scored relatively high on a measure of trait social anxiety symptom severity enrolled in the five-week EMA study (sample size determined with respect to the primary research questions tested in Daniel et al., 2020). Participants were eligible for the study if they scored at least a 29 on the Social Interaction Anxiety Scale (SIAS; Mattick & Clarke, 1998). This measure ranges from 0 to 80 and higher scores indicate greater symptom severity. The cutoff score of 29 was determined a priori to ensure participants were experiencing moderate to severe social anxiety symptoms prior to beginning the parent study, which aimed to test the effectiveness of an online intervention designed to reduce social anxiety. Specifically, 29 represents approximately 25% of a standard deviation below the average score observed in a sample diagnosed with social phobia (M = 34.6, SD = 16.4; Mattick & Clarke, 1998). Participants also had to own an Android or iPhone that was compatible with MetricWire (the EMA mobile phone sampling application used in the study).

One hundred and nine participants were ultimately included in analyses. Reasons for participant exclusion were: n = 1 did not provide sufficient information on the SIAS and so should not have been invited to participate; n = 1 completed the baseline portion of the study unreasonably quickly and using an internally inconsistent response style, suggesting inattentiveness to the study procedures, and was subsequently not invited to participate nor enrolled in the EMA portion of the study (these two reasons for exclusion, though not preregistered, follow precedence set in prior publications from this dataset; e.g., Daniel, Larrazabal, et al., 2023; Daniel, Southward, et al., 2023); n = 3 completed fewer than seven EMA surveys throughout the study and so were considered ineligible for the analyses described below (this reason for exclusion was pre-registered for the present analyses, https://osf.io/yfvbr). Demographic information for the final sample, including descriptive information from the SIAS and state anxiety reports, is provided in Table 1.

Table 1.

Self-Reported Participant Demographics

Demographic Characteristic	N = 109
Social Interaction Anxiety Scale (SIAS)	M = 46.35 (SD = 10.14)
State Anxiety (1-10 scale)
Sample Level	M = 4.11 (SD = 2.41)
Average Participant Level	M = 4.25 (SD = 1.93)
Age	M = 20.45 (SD = 2.97)
Gender
Woman	81 (74.31%)
Man	28 (25.69%)
Nonbinary and other gender identities	0 (0%)
Race
White	75 (68.81%)
Asian	17 (15.60%)
Black	7 (6.42%)
Middle Eastern	2 (1.83%)
Multiracial	8 (7.34%)
Prefer not to answer	0 (0%)
Ethnic Identity
Latinx/Hispanic	3 (2.75%)
Not Latinx/Hispanic	105 (96.33%)
Prefer not to answer	1 (0.92%)
Education Level
Bachelors’ Degree	103 (94.50%)
Master’s Degree	5 (4.59%)
Doctoral Degree	1 (0.92%)

Study Procedure

Data from this study were collected between 2018 and 2019. Participants consented to participate in two 1.5 hour in-lab sessions separated by five weeks of EMA surveys on their personal smartphone. As part of a larger study, approximately half of the participants were randomized to receive an online cognitive bias modification intervention (designed to reduce anxious thinking) half-way through the study period (i.e., during Week 3; see https://osf.io/eprwt/). Within the EMA portion of the study, participants received up to six randomly timed (RT) surveys per day (although participants in the intervention group only received two surveys per day during Week 3 to reduce participant burden), one end-of-day survey, and one end-of week survey for five weeks. MetricWire delivered randomly timed surveys at a random time between each two-hour window from 9am-9pm. As such, the 53 participants randomized to the intervention condition could submit up to 210 RT surveys, and the 56 participants randomized to the control condition could submit up to 182 RT surveys. RT surveys were designed to take less than two minutes to complete and to remain open for up to 45 minutes or until answered. Participants’ compensation for the EMA portion of the study varied based on how many surveys they completed, with potential earnings of up to $80. The current study focuses on data collected during the EMA protocol from the RT surveys. In total, 12,616 RT surveys were submitted by the 109 participants included in the present analyses; the average number of RT surveys submitted per participant was 115.74 (median = 120, SD = 50.75). This represents 59.17% sample-level RT survey compliance and 28.4% of this final sample provided surveys at or above 80% person-level compliance (median = 62.64%, SD = 25.49%, range = 3.81-100%). The average amount of time between successive RT survey responses was 6.96 hours (median = 2.76 hours, SD = 12.40 hours).

Measures

Trait social anxiety symptoms.

Symptoms of social anxiety were assessed using the Social Interaction Anxiety Scale (SIAS; Mattick & Clarke, 1998) prior to beginning the EMA portion of the study. Participants rated their agreement with 20 statements on a 0 (“not at all characteristic of me”) to 4 (“extremely characteristic of me”) Likert scale, with higher scores indicating greater social anxiety symptom severity. Internal consistency in the present sample was good (α = .83).

State anxiety.

At each randomly timed survey, participants rated their momentary anxiety using the single item, “Right now, I am feeling…”,with anchors ranging from 1 (“very calm”) to 10 (“very anxious”). The Spearman-Brown reliability coefficient in the present sample was excellent (ρ_xx’ = 98.). This was determined by dividing the total number of survey responses per participant into two halves using alternating observations and then comparing the within-participant averages across these two halves.

State emotion regulation.

At each randomly timed survey, participants reported their momentary ER strategy attempts throughout the 30-minutes before the survey prompt. Participants could either report that they did not attempt to change their thoughts or feelings, or they could select from 19 unique ER strategies that were displayed using a check-all-that-apply list. These 19 strategies were obtained through a review of the literature (e.g., Heiy & Cheavens, 2014) and in consultation with graduate and undergraduate research assistants. Lay-person descriptions of these strategies, which participants were shown and trained on, along with their conceptual labels, are provided in Table 2. Participants were not limited in the number of strategies they could select at each survey and each endorsed strategy was coded as a 1 (vs. 0). Participants could also report that they were not regulating their emotions at all (also scored as 1 vs. 0 if endorsed) or report that they were using some strategy other than the 19 that were provided.³ Following procedures established in prior studies using these data (e.g., Daniel, Larrazabal, et al., 2023), surveys in which participants both reported not engaging in ER and selected using at least one specific ER strategy were recoded to reflect that some ER strategy had indeed been used at that survey (no changes were made to how the specific ER strategies were scored).

Table 2.

Emotion Regulation Strategy Items

Item Presented to Participants	Conceptual Label
“Ruminating about something.”	Rumination
“Coming up with ideas/plans for action.”	Problem solving
“Accepting them.”	Acceptance
“Criticizing myself.”	Self-criticism
“Thinking of the situation differently.”	Cognitive Reappraisal
“Thinking about the things that went/are going well.”	Thinking good thoughts
“Pushing away bad thoughts.”	Thought Suppression
“Tackling the issue head on.”	Tackling the issue head on
“Distracting myself.”	Distraction
“Drinking alcohol.”	Alcohol
“Using marijuana, nicotine, or other drugs.”	Drugs
“Eating food.”	Eating
“Exercising.”	Exercising
“TV/internet/gaming.”	TV/Gaming
“Sleeping.”	Sleeping
“Seeking advice/comfort from others.”	Advice-seeking
“Ignoring/avoiding certain people/situations.”	Situational avoidance
“Hiding my thoughts/feelings from others.”	Expressive Suppression
“Doing something fun with others.”	Doing Something Fun

Plan for Analyses

Pre-processing Data for ER Stability Calculation.

We used the ‘buildTransArray’ function in the TransitionMetrics package (Daniel & Moulder, 2020) to build a sliding series of transition matrices per participant with 20-by-20 dimensions. The 20-by-20 dimensions reflect all 19 ER strategies plus the “no ER” response option. A transition matrix organizes all switches that occur between back-to-back surveys, where each cell in the matrix maps on to a specific strategy-to-strategy switch. See Appendix A for a simplified example. We decided a priori to include “no ER” in the transition matrix because we conceptualized the propensity to switch between an active response and no ER response as still indicative of regulatory decision making. Along these lines, previous investigations in these data showed that participants reported “no ER” for multiple reasons, including some reasons that relate to difficulties with adaptive switching, such as not knowing what ER strategy to use or feeling that employing a strategy would not be effective (Daniel, Southward, & Teachman, 2023).

We set window size (W) to seven with a lag of 1 so that each transition matrix would be built with surveys from at least two different days, thereby increasing the likelihood that participants would be reporting ER attempts in response to multiple, distinct events. In this context, a “window” refers to the number of surveys that were included in each transition matrix. A lag of 1 means that each participant’s first window captured surveys 1-7, their second window captured surveys 2-8, and so on until their last survey was included in their last window. Setting a sliding window allowed us to calculate multiple stability values for each participant across their whole study, which was necessary to support our within-person hypotheses. The number of transition matrices built per participant varied based on how many total observations they submitted throughout the study.

Empirical Support for Applying Stability to Unequal Time Intervals Data.

Our pseudo-random between-person sampling schedule introduced inconsistencies in the amount of time between survey observations (both within and between people). Given high rates of switching over a brief timeframe might be qualitatively different from the same rate of switching over a longer timeframe, it was important that we tested whether applying the stability metric to data like ours would introduce bias into its measurement or result in a measure that lacked sufficient coverage compared to if we had sampled strategy choice at an equal rate within and between participants. We therefore conducted extensive simulation work to test this question and found robust support that the stability metric is trustworthy (i.e., is unbiased and has approximately 95% coverage) when applied to data collected through within- and between-person random sampling and in data where the probability of any given strategy’s endorsement was determined based on the observed rates of strategy endorsements from a previous EMA study of ER. These results are described more fully by Daniel, Moulder, and colleagues (2023).

Calculating ER Stability.

We used the ‘transStats’ function in the TransitionMetrics package to calculate stability for each transition matrix according to

$$S{t}_{ij}=\frac{tr(X_{ij})}{\sum \sum {\mathbf{X}}_{ij}}$$ (1)

Where $tr(X_{ij})$ is the sum of the elements along the diagonal of a given 20-by-20 transition matrix $X_{\text{ij}};\sum \sum X_{ij}$ is the sum of all elements of X_ij.

Stability was introduced and its psychometric functioning was established in Daniel et al (2022). Stability returns a score that is bounded between 0 and 1. Values closer to 1 indicate that a greater proportion of the observed transitions occurred between the same ER strategy at consecutive time points (relative to switching between different strategies at consecutive time points). As such, values closer to 1 indicate less switching between strategies across those observations (e.g., distraction ➔ distraction ➔ distraction ➔ distraction across four successive surveys would be scored 1). Values closer to 0, by contrast, indicate more switching between different strategies at different time points. Importantly, a stability score of 0 is earned so long as the same strategy is not used at two successive surveys even if the same strategy is reported at some point within the time series window (e.g., distraction ➔ cognitive reappraisal ➔ acceptance ➔ emotion suppression is equivalent to distraction ➔ acceptance ➔ distraction ➔ acceptance; both patterns would earn a stability score of 0). Stability is based on all pairwise transitions, which means it can be applied to data where more than one strategy is endorsed at the same time (see Daniel et al., 2022 for a description and Appendix A for an example of how stability is calculated when strategies can be endorsed simultaneously).

Specifying the Model.

The model is presented in Figure 1 as a path diagram in the structural equation modeling framework using time delay embedding with seven dimensions and a windowing lag of one. ER stability was multiplied by 10 and entered as a time-varying manifest variable in the model. Trait social anxiety symptom severity was entered as a time-invariant manifest variable, grand mean centered, and divided by 10.⁴ We scaled ER stability and trait social anxiety symptom scores in these ways to aid model convergence. State anxiety was person-mean-centered and then put into a seven-dimension time delay embedding matrix to conform to the number of surveys contributing to each stability calculation. The three state anxiety metrics were then specified along the seven dimensions of that time delay embedding matrix. Specifically, mean state anxiety was entered as a latent variable with loadings to all seven state anxiety indicators fixed to one. The first derivative in state anxiety was specified with a loading matrix of {−3, −2, −1, 0, 1, 2, 3} to capture how much anxiety is increasing or decreasing throughout the window. Standard deviation of state anxiety was entered as a time-varying manifest variable that was solved for by taking the standard deviation of the seven state anxiety observations in each row of the time delay embedding matrix. We used identity variables to include the moderation effect of trait social anxiety symptom severity on the relationships between each state anxiety metric and ER strategy stability. Finally, to account for possible cognitive bias modification intervention effects, we included treatment condition as an interaction term throughout the system, where condition was specified using a binary, time-varying indicator (0 for all participants leading up to the intervention beginning in Week 3, 1 for participants randomly assigned to the intervention after Week 3, and 0 for control condition participants after Week 3). Specifically, the condition value used at each window was always associated with the central time point in the time delay embedding matrix.

Figure 1.

Social Anxiety and Emotion Regulation Switching Path Model

Notes. SIAS = Social Interaction Anxiety Scale; Stab = stability in emotion regulation strategy choices solved for along a sliding series of seven successive surveys inclusive; mA = average state anxiety score given by the seven state anxiety scores which are labeled A_i through A_i+6; dxA = first derivative in state anxiety across the same seven state anxiety scores; sdA = standard deviation in state anxiety observed across those same state anxiety scores. Bolded paths were tested for path significance. Significant paths remain in black and include path estimates. Grey paths were not significant.

We conducted analyses in OpenMx version 2.20.6 (Neale et al., 2016) in R version 4.1.3 (R Core Team, 2022). We tested the significance for all hypothesized paths using likelihood-based confidence intervals (the “mxCI” argument in the “mxModel” statement). Paths with 95% CIs that did not include zero are considered significant. Hypothesized paths that were tested for path significance are bolded in Figure 1.

Results

The model depicted in Figure 1 converged without error. Due to a limitation within OpenMx, absolute fit statistics (e.g., RMSEA, CFI) are not available when definition variables are included in the model (which are needed to conduct our tests of moderation, though recent work has introduced an alternative approach to tests of moderation using products of variables; Boker et al., 2023). As such, we do not report absolute fit statistics for the present model. That said, confidence intervals still function as expected for paths within such models and can be interpreted for path significance (Neale & Miller, 1997; Pek & Wu, 2015). See Table 3 for information on all free parameter estimates.

Table 3.

Summary of Free Parameters in Social Anxiety and Emotion Regulation Model

	Estimate	Standard Error	95% CI Lower Bound	95% CI Upper Bound
Paths Assessed for Path Significance
mA ➔ Stability	−.64	.05	−.74	−.54
dxA ➔ Stability	−.15	.36	−.66	.36
sdA ➔ Stability	−1.02	.04	−1.10	−.94
SIAS ➔ Stability	−1.18	.08	−1.33	−1.03
mA * SIAS ➔ Stability	−.14	.05	−.23	−.04
dxA * SIAS ➔ Stability	−.28	.39	−.76	.19
sdA * SIAS ➔ Stability	.41	.04	.33	.50
Additional Paths Included in the Model
mA * Inter ➔ Stability	.09	.12
dxA * Inter ➔ Stability	.59	.71
sdA * Inter ➔ Stability	.32	.04
covariance (mA, dxA)	−.0001	.004
covariance (mA, sdA)	.26	.01
covariance (dxA, sdA)	−.001	.003
covariance (mA, SIAS)	−.001	.02
covariance (dxA, SIAS)	−.0002	.004
covariance (sdA, SIAS)	.14	.01
(Error) Variance Pathsρ
mA_v	.75	.02
dxA_v	.05	.002
sdA_v	.72	.01
SIAS_e	1.02	.001
Stability_e	10.45	.14
Means Paths
sdA	1.61	.01
SIAS	−.00001	.07
Stability	6.30	.07

Notes. mA = mean state anxiety; dxA = first derivative in state anxiety; sdA = standard deviation in state anxiety; SIAS = trait social anxiety measured via the Social Interaction Anxiety Scale; Stability = stability in emotion regulation strategy choices (higher stability denotes less switching and lower stability denotes more switching); Inter = intervention condition; appending a variable name with _v denotes a variance path; appending a variable name with _e denotes an error variance path. Paths are significant if its upper and lower 95% Confidence Interval bounds do not cross 0.

^*is used to reflect an interaction effect between two variables on Stability.

^ρEstimates and standard errors for the seven state anxiety indicators along the time delay embedded matrix are not included to improve readability of model output.

With respect to our between-person hypothesis, participants with higher levels of trait social anxiety severity switched their ER strategies more often across the study than participants with relatively lower levels of trait social anxiety severity. This is consistent with our alternative hypothesis for this effect.

With respect to our within-person hypotheses, periods of relatively higher average state anxiety and periods of relatively more variable state anxiety were associated with higher rates of ER strategy switching, which was consistent with our hypotheses. However, contrary to hypothesis, the association between first derivative in state anxiety and ER stability was not significant.

Two of the three cross-level interactions we tested were significant. First, we observed a significant interaction between trait social anxiety severity and average state anxiety in predicting ER stability. Specifically, participants switched their ER strategies more often when they were experiencing more intense state anxiety, but this effect was especially pronounced in individuals who endorsed higher trait social anxiety severity. This finding is in line with our hypothesis that the effect between average state anxiety and ER switching patterns would be stronger for those with higher (vs. lower) levels of trait social anxiety (see Figure 2A). Second, we observed a significant interaction between trait social anxiety severity and the standard deviation in state anxiety in predicting ER stability. Specifically, participants switched their ER strategies less often when they were experiencing less variability in their state anxiety—which is consistent with our main effect hypothesis—however, counter to what we expected, this effect was especially pronounced in individuals who endorsed lower trait social anxiety severity (see Figure 2B). However, contrary to hypothesis, the interaction between trait social anxiety severity and first derivative in state anxiety was not significant. This means we did not find evidence that the rate at which state anxiety was changing was associated with ER switching (either across the full sample or depending on level of trait social anxiety symptoms) but we did find evidence that people who are relatively more socially anxious may switch between ER strategies more often when they are experiencing relatively higher periods of state anxiety, but not switch their ER strategies as much during periods of relatively high anxiety variability.

Figure 2A. Johnson-Neyman Plot Depicting the Significant Interaction between Trait Social Anxiety Severity and Average State Anxiety Intensity on Stability in Emotion Regulation Strategy Choices.

Note. SIAS = Social Interaction Anxiety Scale in standard deviation units. Negative values on the y-axis indicate switching ER strategies more often when experiencing more intense state anxiety. The dashed segment of the horizontal line at 0.0 reflects the range of SIAS that we do not have in our data.

Figure 2B. Johnson-Neyman Plot Depicting the Significant Interaction between Trait Social Anxiety Severity and Standard Deviation in State Anxiety Intensity on Stability in Emotion Regulation Strategy Choices.

Note. SIAS = Social Interaction Anxiety Scale in standard deviation units. Negative values on the y-axis indicate switching ER strategies more often when experiencing more variable state anxiety. The dashed segment of the horizontal line at 0.0 reflects the range of SIAS that we do not have in our data.

Discussion

The present study applied the stability order-based metric to measure the extent to which socially anxious participants switched between using 19 different ER strategies (or not regulating) in daily life. We tested the average effect across all participants between ER switching and three different metrics that described participants’ self-reported state anxiety throughout the EMA (i.e., average state anxiety, standard deviation in state anxiety, and first derivative in state anxiety). Consistent with our alternative between-person hypothesis, participants with higher levels of trait social anxiety symptoms tended to switch more often between ER strategies throughout the study. Consistent with our within-person hypotheses, participants tended to switch between ER strategies less often when their average state anxiety was less intense and when their state anxiety was less variable—however, these significant main effects were subsumed within significant interactions. Specifically, higher symptoms of trait social anxiety strengthened the observed association between higher average state anxiety and greater ER switching whereas they weakened the observed association between greater state anxiety variability and greater ER switching. The association between how much state anxiety was increasing or decreasing (i.e., the first derivative in state anxiety) and ER switching was neither significant as a main effect nor was it moderated by trait social anxiety.

Higher Average State Anxiety is Associated with Periods of Greater ER Switching

It is not surprising that we observed greater ER switching during periods that were characterized by more intense average state anxiety given strategy selection and implementation follow from an ER goal being prompted by an emotion that differs from what is desired (Gross, 2015). Another possibility is that higher rates of ER switching tended to be less effective, leaving anxiety high or, alternatively, an unmeasured situational variable was also regularly changing during these periods, prompting both different ER choices and exacerbating anxiety. Whatever the reason for this effect, it may have been especially pronounced in our data given that we included “no active ER attempt” as a response option (alongside all 19 ER strategies) in the transition matrix used to calculate stability. Periods of low average state anxiety are predictably characterized by a greater likelihood of “no ER” responses (Daniel, Southward, & Teachman, 2023), and recurrent “no ER” responses yield a higher ER stability/lower switching value. Further, we know from the polyregulation literature that people typically use more than one ER strategy when regulating more intensely negative state affect (Ladis et al., 2022), and use of multiple strategies is tied to decreased stability/higher switching (Daniel et al., 2022).

The relationship we observed between average state anxiety and ER switching was especially pronounced in individuals who endorsed higher trait social anxiety severity. This moderation effect was in line with our hypothesis and suggests that people with higher social anxiety might engage in a frantic search across strategies to reduce their distress, whereas people with less severe trait social anxiety may be better able to ‘stay the course’ with their initial strategy selections. An alternative interpretation is that socially anxious people are less effective at reducing their state anxiety across all strategies, so their switches are less useful. Indeed, our findings highlight yet another way in which low distress tolerance amongst people with elevated social anxiety symptoms may manifest in their daily life ER patterns. Similarly, Goodman and colleagues (2021) found that socially anxious people use more strategies than healthy control participants in response to stressful events. Further, in the same data used here, we found that social anxiety severity was positively associated with using a more diverse, even, and frequent range of ER strategies throughout the first two weeks of the EMA study after controlling for state anxiety (Daniel, Larrazabal, et al., 2023). The current work extends this earlier work by linking strategy choices together sequentially. Yet, despite using different methods, all three analyses converge on the interpretation that socially anxious people may not rigidly engage in avoidant-specific ER responses in daily life. Rather, they may shift between many different ER strategies with perhaps too little persistence and skill.

Extending this work to account for co-occurring changes in relevant situational demands (e.g., changing social contexts) may further elucidate the relationship between trait social anxiety, state anxiety, and ER choice. For example, perhaps less socially anxious people remain in the same social setting for longer than more socially anxious people due to a lower tendency to feel distress and ultimately escape social situations; if true, this could contribute to a more comprehensive understanding of why more socially anxious people appear to switch their ER strategies more often when feeling more anxious.

Higher Standard Deviation in State Anxiety is Associated with Periods of Greater ER Switching

As expected, when state anxiety was more variable over a given period (indicated by a higher standard deviation), participants in our sample tended to switch between ER strategies more often. This effect might be explained by participants switching between reporting “no ER” and some ER strategy when state anxiety varied between low and moderate/high values, respectively (Daniel, Southward, & Teachman, 2023), and by participants switching between certain ER strategies (e.g., reappraisal and distraction) when state anxiety varied between moderate and high state anxiety reports, respectively (Sheppes et al., 2014). This effect might also be explained by different strategies changing anxiety to different degrees or by a higher instance of change in an unmeasured situational variable (e.g., number of social interaction partners), prompting both different ER choices and different levels of anxiety during these periods.

Whatever the explanation may be, this relationship was moderated by trait social anxiety severity such that, unexpectedly, participants with higher levels of social anxiety did not demonstrate as strong an association. Although people with low levels of social anxiety symptoms were not included in the sample and our analyses do not explicitly test how well strategy choices matched different contexts, our findings lead us to speculate that participants with especially high levels of trait social anxiety may have trouble modulating ER responses in response to varying levels of state anxiety intensity or have similar emotional responses to different ER strategies. One possibility is they treat many levels of state anxiety as exceeding a threshold of aversiveness that warrants a change in ER strategy because they are so eager to reduce all anxiety. Indeed, there is some work suggesting that adults with social anxiety disorder have trouble differentiating between negative emotions (Kashdan & Farmer, 2014). As such, they may not show the normative pattern of choosing different ER strategies depending on the relative intensity of their state anxiety (Birk & Bonanno, 2016; Sheppes et al., 2014). That said, our design cannot rule out the possibility that these findings are best explained by co-occurring changes in relevant situational contexts. Moreover, future work that operationalizes anxiety variability through order-based metrics, such as those measuring affect instability (root mean square of the successive differences, probability of acute change, the Teager-Kaiser energy operator) and inertia (i.e., autocorrelation) would be interesting.

First Derivative in State Anxiety is Not Associated with Degree of ER Switching

Unexpectedly, we did not find an association between how much state anxiety was increasing or decreasing and ER switching in our sample. This null result may in part be explained by the timescale at which we sampled. By sampling every few hours and across days, we likely captured regulation across distinct emotional events (rather than ongoing regulation attempts in response to the same emotional event). Although some stressors are likely regulated over longer time frames (e.g., an upcoming test, a big fight with a significant other), Farmer and Kashdan (2015) found that socially anxious people report more negative interpersonal events per day than do healthy control participants, suggesting social anxiety is associated with relatively quick shifts to new emotional events. Thus, our sampling rate may have missed the chance to catch shorter-term change in state anxiety and ER switches within a single event. It is possible that a different study design—for example, one where participants were asked every few minutes how they were feeling and how they were regulating following a single stressor—would be better positioned to uncover relationships between increasing/decreasing anxiety and a switch/no switch in ER strategies.

Interestingly, unlike the current null result (that was found when state anxiety change and ER switching were examined concurrently), previous analyses in the same dataset that looked at how degree of ER switching predicted subsequent state anxiety change found that periods of less strategy switching preceded a subsequent steeper decline in state anxiety intensity as measured at the next survey (Daniel et al., 2022). Timing differences likely explain the different results—whereas the current study analysis investigated rate of change in state anxiety over the same seven EMA surveys that ER switching was measured, Daniel et al. (2022) looked at how ER switching over six successive EMA surveys predicted a single observation of state anxiety at the very next EMA survey (e.g., stability calculated over surveys 1-6 predicted anxiety at survey 7 after accounting for anxiety at survey 6). Combining these results, it seems that if a person has recently not been switching between ER strategies very often, this does not relate to how much their state anxiety is simultaneously increasing or decreasing. However, after a person has settled into a period of relatively stable ER strategy choices, they may be about to have a break from anxiety. The collected findings raise intriguing questions about when changes in state anxiety and ER strategy switches will have concurrent versus lagged effects on one another, but future research is needed to understand these relationships more fully.

Clinical Implications

First, we found that social anxiety severity strengthens the association between higher average state anxiety and greater ER switching. Though alternative explanations are possible, if this finding is in fact due to highly socially anxious people frantically switching strategies to reduce their anxiety as quickly as possible, then clinicians may wish to help socially anxious clients build perseverance in using ER strategies that are likely to promote their long-term goals, even if using that strategy does not immediately reduce anxiety. This emphasis could directly complement work on increasing distress tolerance, a mechanism of change often targeted in the treatment of anxiety disorders (Ranney et al., 2022). However, for strategy perseverance to be beneficial, the initial strategy must be well matched to the situation and the person’s long-term goals, as well as be skillfully implemented.

Second, we found that social anxiety severity weakens the association between greater state anxiety variability and greater ER switching. Though alternative explanations are possible, if this finding is in fact due to highly socially anxious people finding it hard to modulate their ER responses based on differing levels of state anxiety intensity because they experience many levels of anxiety as similarly aversive, then clinicians may wish to help clients identify what level of emotional intensity they are experiencing and what an appropriately matched strategy is to that intensity. This emphasis could complement emotion awareness- and emotion differentiation-related interventions that are often integrated into the treatment of social anxiety disorder (e.g., cognitive behavioral therapy, acceptance and commitment therapy, emotion focused therapy).

Limitations and Future Directions

This study only includes individuals with elevated symptoms of social anxiety. Although we still retained meaningful between-person variance in ER and state anxiety, this inclusion criterion restricted our range somewhat on this component of the model. While there are advantages to using this population (i.e., this is a highly prevalent disorder characterized by rigid ER and emotion dysregulation; Jazaieri et al., 2014; NICE, 2013), the patterns we observed may not generalize to people with other forms of psychopathology or to psychologically healthy individuals. Further, due to a restriction in the range of social anxiety symptoms, certain between-person effects of trait social anxiety symptom severity may not be apparent in our data. Relatedly, our sample is largely female, non-Hispanic White, young, and highly educated. As such, our findings may not generalize to individuals holding other identities. Additionally, while all participants were living in the Southeastern United States during their study participation, we did not gather information regarding participants’ cultural backgrounds, which further limits the generalizability of these findings. Future research is needed in clinical and more diverse, representative samples; as well as in samples that vary in their level of introspection and ER knowledge, as these between-person characteristics might impact how accurately participants are able to report on their ER attempts.

Second, we used EMA data collected on a randomly timed survey schedule, so it is unlikely that all strategy choices a person made throughout their day were reflected in the data (i.e., a person might have switched their ER strategies many times between two successive surveys). Relatedly, our sampling rate is on the time scale of hours (at a minimum) and days (at a maximum, due to missing survey responses). Attending to the sampling frequency is important because, if a given order of strategy choices is made over the span of minutes, it is likely a qualitatively different experience than if the same order of strategy choices were made over the span of hours. Indeed, one vignette-based study found evidence to suggest that changing strategies within one situation (i.e., at a shorter timeframe) is not as helpful as changing strategies between different situations (i.e., at a longer timeframe; Southward et al., 2018). Future designs that distinguish between ER switching when it occurs across different stressors versus when it occurs throughout the regulation of a single stressor could help deepen our understanding of how perseverance in ER strategy use versus context-sensitive responsiveness to affective feedback relate to mental health and wellbeing.

Third, participants varied widely in how many surveys they submitted throughout this five-week data collection (M = 112.81, SD = 53, range = 3, 205). It is reasonable to assume that at least some of the differences observed in number of submitted survey responses can be explained by meaningful individual differences (i.e., level of conscientiousness) or circumstances participants were in when surveys were delivered to their phone (i.e., when in class vs. when at home). If missing a survey is related to variables that also relate to how someone would have responded to the survey, then this pattern of missingness will likely bias parameter estimation (Schafer, 1997). While multiple imputation can soften the impact of such biases in certain circumstances, a previous simulation study showed that time delay embedding—which was used in this analysis—was robust to such biases and not significantly improved upon by incorporating additional sophisticated full information maximum likelihood correction procedures (Boker et al., 2018). As such, we decided to use all submitted surveys without imputing. Also, we used full information maximum likelihood estimation procedures, which helps to reduce bias from the rare cases of item-level missingness observed in our data.

Fourth, our models estimate the average effect across all participants in our sample. Estimating this model in a multilevel SEM framework may offer interesting insights by teasing apart within and between person variances. However, due to the complexity of our model and novelty of the switching metric used, we decided to focus first on sample-wide average effects to lay an initial foundation. Related to novel measurement, a proliferation of newer ER-related metrics has recently emerged (e.g., Spread: Daniel et al., 2022; Bray-Curtis Dissimilarity: Lo et al., in press; ER Diversity: Wen et al., 2021) in addition to Stability. An important next step will be to compare these metrics to one another both empirically (in simulated and real data) and theoretically (e.g., ER Diversity does not incorporate a time-ordered component to its calculation like the other three metrics do; Stability and Spread is designed for binary measurement of ER strategy use whereas ER Diversity and Bray-Curtis Dissimilarity can be applied to data when ER use is measured continuously). Such future work could help to develop guidelines for researchers around which metrics are best suited to which research questions and data characteristics.

Fifth, although we used an inclusive list of 19 strategies, this list is not exhaustive and there may be important overlap among the included strategies. For example, four successive responses of “TV/gaming” ➔ “distraction” ➔ “TV/gaming” ➔ “distraction” would be rated by the stability metric as evidencing the highest rate of strategy switching possible. Yet, if the participant was engaging in “TV/gaming” as a means of distracting themselves, one could reasonably argue that this pattern does not reflect high switching. However, if the participant’s use of “TV/gaming” was to serve other functions (e.g., to build a sense of mastery, to connect with others, to do something enjoyable), then perhaps the high switching interpretation is appropriate. This raises important considerations about what an exhaustive but not redundant set of ER strategies is; and how to incorporate changing motivations behind, or different functions of, a given strategy.

Finally, people do not update their ER strategies only in response to how their state anxiety changes. People also choose ER strategies in response to changes in their goals (Tamir et al., 2013) and external environments (Bonanno & Burton, 2013). These external environments also influence the helpfulness of any given strategy (Gross, 2015) and certain ER strategies may be more feasible in some contexts over others (e.g., Suri et al., 2018). Thus, to further understand patterns in ER switching, it will also be interesting to consider ER strategy choices as a person moves into and out of various contexts throughout daily life (see McKone et al., 2022, for an early example of this important next step) and as they experience a full range of emotions beyond only anxiety. These extensions are needed to ultimately make ER switching recommendations that will make a meaningful impact on mental health functioning.

Despite these limitations, this study helps the field take a new step towards conceptualizing and measuring ER switching in daily life. We hope this work will encourage future data collections that increase ER sampling frequency throughout the time course surrounding a given stressor to further elucidate patterns in ER switching within and between different types of stressors.

Conclusions

The present study applied a new order-based metric—called stability—to measure the extent to which socially anxious individuals switched ER strategies throughout a five-week EMA study. We found that participants with higher (vs. lower) levels of trait social anxiety symptoms switch ER strategies more often during periods of relatively more intense state anxiety and less often during periods of relatively more variable state anxiety. Our findings are consistent with the idea that people with relatively higher social anxiety symptoms may flail between ER strategies during periods of high state anxiety and fail to use changes in state anxiety to guide strategic ER switching decisions. Both findings point towards potential problems with effectively switching between ER strategies amongst people with elevated social anxiety symptoms that might be explained by deficits that are implicated not only in this highly prevalent disorder, but also across internalizing psychopathology more broadly (e.g., low distress tolerance and difficulty with emotion differentiation). Expanding this work to consider the role of changing situational demands will deepen our understanding of these findings, potentially highlighting important opportunities for clinical intervention. Making wise decisions about when to switch ER strategies and when to remain stable is a fundamental challenge for healthy ER.

Appendix A

To demonstrate the mechanics of our stability method, we now share a verbal description of this process using a simple case alongside a visual representation in Figure A1. Imagine a participant i rated whether or not they used each of four different ER strategies (ER₁, ER₂, ER₃, ER₄) at 8 time points (T₁, T₂, T₃, T₄, T₅, T₆, T₇, T₈). With these data, assuming a window of 7 and a lag of 1, we can construct two transition matrices (X_i1, X_i2).

Figure A1. Visual Demonstration of Method.

Note. Two transition matrices constructed from example data with 8 observations (T₁ through T₈), window size of 7 observations per transition matrix, four binary time series (ER₁ through ER₄), and a windowing lag of one. We chose not to reduce the stability fractions, when appropriate, to avoid obscuring the relationship between the matrices and the resulting values.

To construct X_i1, we would start by creating a 4 x 4 matrix for which all elements are initialized to zero. The example data show that ER₁ and ER₃ occurred at the first observation (T₁) and ER₃ occurred again at the second observation (T₂). This means that a pairwise transition from ER₁ to ER₃ and a pairwise transition from ER₃ to ER₃ occurred between the first two time points. Thus, we increment the (3,1) element of X_i1 by one (to reflect the transition from ER₁ to ER₃) and we increment the (3,3) element of X_i1 by one (to reflect the transition from ER₃ to ER₃). All other elements remain at 0. At the next observation (T₃), ER₃ and ER₄ were both endorsed, indicating that a pairwise transition from ER₃ to ER₃ and a pairwise transition from ER₃ to ER₄ occurred between T₂ and T₃. To reflect these two pairwise transitions, we increment the (3,3) element of X_i1 by one (to reflect the transition from ER₃ to ER₃), such that the (3,3) element now equals two, and we increment the (4,3) element of X_i1 by one (to reflect the transition from ER₃ to ER₄). At the next observation (T₄), ER₁ was the only variable endorsed, indicating that a pairwise transition from k₃ to k₁ and a pairwise transition from k₄ to k₁ occurred between T₃ and T₄. Thus, we increment the (1,3) element of X_i1 by one (to reflect the transition from ER₃ to ER₁) and the (1,4) element of X_i1 by one (to reflect the transition from ER₄ to ER₁). At the next observation (T₅), ER₃ was the only variable endorsed, indicating that a transition from ER₁ to ER₃ occurred between T₄ and T₅. Thus, we increment the (3,1) element of X_i1 by one, such that the (3,1) element now equals two. At the next observation (T₆), ER₃ was the only variable endorsed, indicating that a transition from ER₃ to ER₃ occurred between T₅ and T₆. Thus, we increment the (3,3) element of X_i1 by one, such that the (3,3) element now equals three. At the next observation (T₇), ER₃ was the only variable endorsed, indicating that a transition from ER₃ to ER₃ occurred between T₆ and T₇. Thus, we increment the (3,3) element of X_i1 by one, such that the (3,1) element now equals four. At this point, all transitions between the four binary variables across the first seven time points are reflected in X_i1 (see Figure A1).

To construct X_i2 we would start with a second 4 x 4 matrix, also initialized to zero. The window of observations being read into X_i2 would be shifted down the time series by one compared to what was read into X_i1, such that the transitions between T₁ and T₂ described above would not be captured by the new matrix. The transitions between T₂ and T₃, T₃ and T₄, and T₄ and T₅, T₅ and T₆, and T₆ and T₇, however, would be incremented into the new matrix like in X_i1. Finally, because the window of observations was shifted down one, there would be one new transition to add to X_i2 (i.e., the transition between T₇ and T₈). In these example data, ER₃ was the only time series variable reported at T₈, indicating that a transition from ER₃ to ER₃ occurred between T₇ and T₈. Thus, we increment the (3,3) element of X_i2 by one, such that the (3,3) element now equals four. At this point, all transitions between the four binary variables across the next seven time points are reflected in X_i2 (see Figure A1).

The stability equation is then applied to these two populated transition matrices, yielding a stability of .444 for X_i1 and .5 for X_i2.

For additional information, please refer to the publication introducing this method (Daniel et al., 2022).