Mind-wandering rates fluctuate across the day: evidence from an experience-sampling study

The present study

Here we investigate the patterns of mind-wandering across the day in two experience-sampling studies. Study 1 focuses specifically on freely moving thought: participants were probed randomly throughout the day for five days on their cell phones as they went about their regular routines. We hypothesized that ratings of freely moving thought would significantly fluctuate throughout the day.

In Study 2, we present a new analysis of a previously published experience-sampling dataset (Mills, Raffaelli, et al., 2017) in an attempt to replicate findings from Study 1. We also ask whether different conceptualizations of mind-wandering (i.e. freely moving thought, task-unrelated thought, and stimulus-independent thought) exhibit different fluctuations over the course of the day. This idea is inspired by Mills, Raffaelli, et al.’s (2017) original finding of low overall correspondence between these distinct forms of mind-wandering; the present study, then, builds on that work to explore whether they share similar dynamics.

In the interest of open science, we have made our code and data freely available on the Open Science Framework (https://osf.io/es3gf/), and our code is additionally available on GitHub (https://github.com/galagon/mind-wandering-fluctuations).

Study 1

Approach to data analyses

Our central research question was to determine if ratings of freely moving thought fluctuate in reliable patterns over the course of the day. To answer this question, we modeled ratings of freely moving thought with the hypothesis that they would vary as a function of time. We used a mixed-effect multilevel modelling approach to test this hypothesis because: (1) it assesses change over time while preserving between-participant differences in baseline ratings (intercept) and estimated relationships (slope; Fuller-Tyszkiewicz et al., 2017); and (2) it is robust to missing data (Mirman, 2016). Below, we describe our analytical approach using current best-practices for growth curve modeling; interested readers can find more detail in Mirman (2016), Mirman, Dixon, and Magnuson (2008), and Singer and Willett (2003).

We tested the patterns of freely moving thought ratings by constructing a mixed-effects model with first- through third-order orthogonal polynomial terms (for comparative examples of the three orders of polynomial models; see Fig. 1). All polynomial terms were orthogonalized to avoid multicollinearity and to ensure independence from one another (see Mirman, 2016). The significance of each term would shed light on a specific pattern, though none are mutually exclusive (see Fig. 1):

1. 1)

   the linear term (first order) would represent a general increase or decrease in freely moving thought over the day;

    
2. 2)

   the quadratic term (second order) would fit the data if ratings were higher or lower in the middle of the day as compared to morning and evening; and

    
3. 3)

   the cubic term (third order) would capture trends that changed direction twice over the day—for example, if the ratings rose throughout the morning, fell in early afternoon (i.e. first change in direction), and rose again through the evening (i.e. second change in direction).

    

We used polynomials to model change across time for three reasons, aside from such models being commonly used in the analysis of temporal dynamics (Hartmann et al., 2016; Mirman et al., 2008; Papageorghiou et al., 2014; Shin, 2012; White, Xie, Thompson, Loeber, & Stouthamer-Loeber, 2001). First, they can easily be orthogonalized with respect to one another, allowing us to interpret the individual contributions of each polynomial without the issue of collinearity. Second, they represent increasingly complex forms of change over time, which is important as we did not believe that simple patterns of change (e.g. linear) were likely given the literature on daily fluctuations of other cognitive variables (Burke, Scheer, Ronda, Czeisler, & Wright, 2015; Fimm & Blankenheim, 2016; Folkard & Monk, 1987; Giambra, Rosenberg, Kasper, Yee, & Sack, 1989; Goel, Basner, Rao, & Dinges, 2013; Riley, Esterman, Fortenbaugh, & DeGutis, 2017; Silva, Wang, Ronda, Wyatt, & Duffy, 2010; Valdez et al., 2005).

Finally, modeling data with these three polynomials served as a first step in understanding the dynamics of mind-wandering using some of the simplest and most commonly used forms of change found in other diurnal cognitive studies. Given the lack of previous work in this domain, we had no reason to suspect that any more complicated time-varying forms of change would provide a better fit; therefore, the choice of more specific and nuanced models would have been arbitrary. While some past studies have attempted to precisely and mechanistically model daily change in a cognitive outcome variable (Jewett & Kronauer, 1999), such models were based upon a deep and established literature that does not yet exist for freely moving thought.

Study 2: reanalysis of Mills, Raffaelli, et al. (2017)

Demonstrating replicability of the results from Study 1 would be highly desirable given the novelty of the research question and the exploratory nature of interpreting polynomial models assessing changes over time. Towards this goal, we conducted a novel analysis of data from Mills, Raffaelli, et al. (2017), a published experience-sampling study in everyday life that included probe timestamp information that had never been analyzed. Reanalyzing this dataset also enabled us to address the question of whether three distinct conceptualizations of mind-wandering (freely moving thought, task-unrelated thought, and stimulus-independent thought) displayed dissociable fluctuations across the day.

Corpus

A complete description of the method from the original study can be found in Mills, Raffaelli, et al. (2017), but we provide a very brief overview here. The methodology was identical to that used in the Study 1 with four exceptions. First, the sample included 226 people initially, with 165 participants retained after removing those who answered 60% or fewer probes completely. Second, probes were given 10 times a day for a period of 10 days, yielding a maximum of 100 probes per participant (the same per-participant maximum as Study 1). Third, the questions concerning sleep and wake time were not included; instead, every probe asked participants to rate their task-unrelated thought (“Were you thinking about something other than what you were doing?”) and stimulus-independent thought (reverse-coded; “Were you aware of your surroundings?”) on a scale of 1 to 7. (Probes also included other questions that were not relevant to the present study; see Mills, Raffaelli, et al., 2017.) Fourth, participants received probes all days of the week but only between the hours of 08:00 and 23:00 (all times local and in the 24-h clock).

Data preparation and analysis

Similar to the analytical approach in Study 1, probes were rounded down to the hour and aggregated by person and hour. Unlike the original study, the probed hours were in the range of 08:00 to 23:00 (Mills, Raffaelli, et al., 2017). Only hour 23:00 was removed as it contained responses from < 25% of participants (Table 1). Figure 3 displays the mean ratings for each hour of the day for each dimension.

Statistical analyses were conducted with the same packages in R (lme4, Bates et al., 2015; lmerTest, Kuznetsova et al., 2017), the same fixed and random effect constraints, the same maximum likelihood effect estimation, and the same unstructured covariance structure as used with the original data. Again, all data were standardized before entry in the model, resulting in standardized (β) rather than unstandardized (B) coefficients. As with Study 1, hierarchical models were created with increasing orders of polynomial time-varying factors and compared on goodness of fit; the results of these comparisons as well as graphics representing the fitted values for each model can be found in our supplementary materials (Additional file 1).

Freely moving thought (Table 3)

Findings for freely moving thought closely replicated results from Study 1. As in the original dataset, both the quadratic and cubic terms reached significance, but the linear term did not. Notably, when the analyses were run without the removal of participants who did not answer a sufficient number of probes, the linear term became significantly positive, likely as the result of higher freedom-movement ratings in the latest hours (for more, see supplementary materials (Additional file 1).

Task-unrelated thought

Ratings of task-unrelated thought showed linear change over the course of the day, but no other time-varying model parameters achieved significance (Table 4). The positive linear parameter indicates that the ratings increased significantly between the beginning and the end of the day. This contrasts with ratings of freely-moving thoughts, which showed quadratic and cubic change but not linear.

Stimulus-independent thought

Ratings of stimulus-independent thought showed similar patterns of change over the day as freely moving thought, exhibiting quadratic and cubic fluctuation without linear change (Table 5).

Comparing different dimensions of thought

Mills, Raffaelli, et al. (2017) found that freely moving thought could be distinguished from content-based definitions of mind-wandering (i.e. task-unrelated thought and stimulus-independent thought). In the present study, we provide a novel test of this claim by assessing whether these three dimensions of thought exhibit differential patterns of change across the day. Although we found that two of the dimensions (freedom-of-movement and stimulus-independence) showed similar patterns of change with the same model parameters being significant for each dimension, the individual slopes that make up the equations may be significantly different. In other words, the steepness of the curves may differ.

We tested this possibility by combining responses to all three questions in a dataset with a three-level categorical variable that we call thought dimension (Table 6). We then created a cubic model that included the main effect of thought dimension and its interactions with each of the three time terms. A non-significant interaction between thought dimension and a time term indicates that the given slope does not differ substantially between the three dimensions of thought, whereas a significant interaction indicates that the dimensions have dissociable slopes.

By default, the lmer function of the lme4 package in R uses treatment contrasts, meaning that it treats interactions involving categorical variables as pairwise comparisons between the first entered level of the variable (in this case, ratings of freely moving thought) and each level after that (task-unrelatedness and stimulus-independence). An analysis comparing task-unrelatedness and stimulus-independence directly can be found in the supplementary materials (Additional file 1), though we chose not to include it in the main text both to minimize the number of tables and to focus on our main research question: does freely moving thought have a distinct daily pattern compared to the dominant, content-based conceptualizations of mind-wandering?

Although there were no significant interactions between dimensions of thought and the linear or cubic terms, the results show an interaction between the quadratic term and the dimension variable with both comparisons reaching significance. The quadratic slope for ratings of freely moving thought was significantly steeper (i.e. more negative) than that of task-unrelated thought yet significantly shallower (i.e. less negative) than that of stimulus-independence thought. This pattern can be observed through visual inspection of the data (Fig. 3): freely moving thought ratings experience a rise and fall pattern over the course of the day and peak close to the middle of the day, a relationship that is exaggerated for stimulus-independent thought and absent for task-unrelated thought.

These differences in changes across the day further highlight the dissociability of the three dimensions and indicate that they may be associated with only partially overlapping neural processes or may arise from distinct constraints on agent-environment interactions.

Weekend-only analysis

The greatest advantage of everyday life experience sampling—the fact that ratings come from participants living their daily lives and not conducting artificial laboratory tasks—comes with its own set of limitations. Without controlling the conditions under which participants answer, it is difficult to know whether the observed fluctuations are caused by intrinsic mechanisms such as diurnal rhythms or whether they are simply the product of the activities in which participants were more or less likely to be engaged in at different points in the day. For example, ratings of freely moving thought were highest around midday, a time when the study’s participants—undergraduate students—would be more likely to be in the middle of classes as compared to the evening or early morning. Aside from classes, this pattern could be driven by participants taking lunch breaks around the noon hour or, conversely, by exhaustion after long periods of intensive effort exerted in morning classes.

Although the primary goal of the study was to determine whether reliable daily fluctuations exist and not to determine their source, the reanalyzed dataset affords the opportunity to examine weekdays and weekend days separately. This exploratory analysis rests on the tentative assumption that daily activities on weekdays (e.g. classes, work) are scheduled differently than weekends for most participants. Thus, if daily fluctuations in thought are identical across weekdays and weekend days despite those days containing different sets of activities, there is evidence that activities alone may not account for these daily patterns of thought.

After removing probes answered during weekdays, 4305 of the original 12,997 probes (33.12%) remained. In order to keep the results comparable, the same participants in the full analyses were used for the weekend-only analyses, regardless of the number of probes answered after the removal of weekday probes. The analysis was limited to the reanalyzed dataset from Mills, Raffaelli, et al. (2017) due to an insufficient number of probes answered over weekend days in the dataset from Study 1.

All model results are available in Appendix 3. For brevity and clarity, we do not include most test statistics in the text, but graphical representations of the data and optimal cubic models can be seen in Fig. 4. The model for freely moving thought revealed a highly similar pattern of results, but neither the quadratic nor the cubic term quite reached statistical significance (quadratic: p = 0.056, cubic: p = 0.054; Fig. 4a). Although the lack of significance at α = 0.05 may indeed indicate a different pattern of fluctuation across the day, the loss of power accompanying a threefold reduction in the number of probes entered into the model may be an alternative reason for this disparity, especially given that the p values in question, while no longer significant, are still < 0.06. While we cautiously interpret the pattern for freely moving thought to be similar for the weekend-only analysis, future work with greater statistical power may be able to shed more light on this possibility.

On the other hand, we were unable to replicate the findings for the two content-based dimensions of thought. In the model predicting task-unrelatedness of thought, no time-varying parameters reached significance. In the model predicting stimulus-independence of thought, the positive linear term reached significance and the positive cubic term no longer reached significance (although it trended toward significance in the same direction), while the quadratic term remained negative and significant.

We note, however, that visual inspection of the weekend-only data indicates a highly similar pattern for task-unrelatedness of thought (Fig. 4b). This again suggests that the difference from the original analysis is possibly the result of power loss (though it is worth noting that in this case the linear term did not trend towards significance). The stimulus-independence data, on the other hand, does appear to exhibit a different relationship (Fig. 4c). Visual inspection indicates that stimulus-independence scores are higher in the evenings, which would account for the increase in the strength of the linear parameter (since the scores at the end of the day are now higher than the those at the beginning) as well as the attenuation of the cubic parameter (since the scores remain comparatively stable after midday and do not dip in the afternoon or evening).

General discussion

Here, we presented—for the first time—evidence that thought patterns fluctuate across the day. Capturing the “wandering” mind by measuring freely moving thought, we probed people on their smartphones during their daily lives to understand the daily rhythms of thought in the “wild.” We found that freely moving thought occurs at lower rates early in the day, rises until midday, and declines gradually before rising once more in the evening. By reanalyzing a dataset from Mills, Raffaelli, et al. (2017), we were able to replicate these results and investigate novel questions about the dynamics of specific kinds of mind-wandering—in particular, we found that freely moving thought showed distinct daily patterns from two other dominant conceptualizations of mind-wandering. Such findings are consistent with a host of previous research showing that human cognition exhibits diurnal dynamics, not uniform properties over time.

What might drive diurnal dynamics?

Although these results provide novel evidence that mind-wandering does dynamically fluctuate throughout the day, they do not speak to why these changes occur. We describe a few possible—but not mutually exclusive—explanations for the patterns of change. However, we recognize that much more work is required to elucidate the mechanisms driving these results, and we present these as testable hypotheses for additional future work.

The first potential mechanism is autonomic arousal. Arousal may bias attentional selectivity by way of the locus coeruleus, a remarkably well-connected norepinephrinergic brain region (Aston-Jones & Cohen, 2005; Aston-Jones & Waterhouse, 2016; Gilzenrat, Nieuwenhuis, Jepma, & Cohen, 2010; Mather, Clewett, Sakaki, & Harley, 2016). Although a direct link between arousal and the freely moving thought conceptualization of mind wandering has not been established, Mittner, Hawkins, Boekel, and Forstmann (2016) recently suggested that levels of norepinephrine originating from the locus coeruleus may differentiate between mental states that are focused on a single subject (regardless of whether the subject is the task at hand) and “exploratory,” unstable states—similar to the distinction between constrained and freely moving thought.

Indeed, diurnal fluctuations in norepinephrine align well with the pattern of results found here: an increase early in the day, a lunchtime peak, and a gradual afternoon/evening decline (Fibiger, Singer, Miller, Armstrong, & Datar, 1984; Hansen, Garde, Skovgaard, & Christensen, 2001). Previously observed fluctuations do not map perfectly onto the cubic structure of mind-wandering observed in the present dataset, given that levels of norepinephrine generally do not increase over the course of the evening. However, both share noticeable similarities throughout the rest of the day. The same pattern exists for attentional performance as well (Carrier & Monk, 2000; Silva et al., 2010; Valdez et al., 2005), suggesting that arousal may be a common mechanism behind these daily changes.

The arousal-based account may also be able to partially explain a somewhat-paradoxical finding from our study: mind-wandering rates tended to be at their highest during the times when past studies have indicated attentional abilities are at their peak and they tended to be at their lowest during the times when attentional performance is purported to suffer (Carrier & Monk, 2000; Folkard & Monk, 1987; Valdez et al., 2005). This co-fluctuation seems counter-intuitive, as the relationship between mind-wandering and performance on sustained attention tasks is often considered antithetical (McVay & Kane, 2009; Smallwood, Fitzgerald, et al., 2009; Stawarczyk et al., 2011). However, it is important to note that the majority of the studies that have found evidence of such an antithetical relationship have used task-unrelated thought as their definition of mind-wandering (oftentimes quite literally operationalized as the inverse of attentional performance); by contrast, freedom-of-movement of thought and attentional performance may not exhibit such a marked negative relationship. In light of this, the observed results would be perfectly in line with an arousal mechanism that impacts both attentional performance and thought dynamics but has no direct impact on the content of thought (or, at the least, not its task-relevance).

A second, simpler explanation for the observed daily fluctuations in mind-wandering may be circumstance or environmental pressure. Ratings of freely moving thought first peaked at the time of day when many participants (all of whom were students) would be in class and ratings dipped at times when they were would more likely to be home. It is therefore possible that the classroom environment may loosen constraints on thought or that other activities or states experienced at certain times of day produce the patterns seen here. Since we did not ask students to report their current activity at the time of each probe, this possibility cannot be completely discounted. However, findings for freely moving thought were partially replicated in a subset of the reanalyzed data that included only weekend days, suggesting that this pattern of change is likely independent of the day of the week, which one would not expect if it was driven by activities.

Finally, mind-wandering fluctuations may be tied to humans’ circadian rhythm in some other way. In two out of three dimensions of thought, we observed a rise-and-fall pattern that mirrors circadian body temperature changes that, in the past, have frequently been found to correlate with cognitive performance in a variety of domains (Carrier & Monk, 2000; Fimm, Brand, & Spijkers, 2016; Goel et al., 2013; Valdez, Reilly, & Waterhouse, 2008; Wright, Hull, & Czeisler, 2002). Although it would have been impractical to record temperature in an everyday life experience-sampling study, there is room for future experimental research to elaborate on the current findings by determining whether freely moving thought exhibits the same correlation with core body temperature as attention, spatial awareness, and other cognitive variables.

We recognize that our study is unable to answer these questions definitively. Perhaps some, all, or none of these explanations even work together: for example, arousal’s influence on mind-wandering could be dependent on current activity or level of motivation. As a result, we call for future work to collect the information that would be able to disentangle these effects, including concurrent measures of arousal, motivation, physiological states, and information about what participants are doing at the time of the probe responses. Such work should also continue to explore the dynamics of the three types of mind-wandering to see how, whether, and when they differ from one another.

Implications

This paper lays the groundwork for understanding daily fluctuations in mind-wandering—a topic that may have implications for shaping real-world policy. Indeed, there is already ample evidence linking one dimension of thought related to mind-wandering (task-unrelatedness) to affect (Killingsworth & Gilbert, 2010), creativity (Baird et al., 2012), and—perhaps most compellingly for public policy—impaired comprehension and classroom performance (Mills et al., 2017; Mrazek et al., 2017; Pachai et al., 2016; Seli, Wammes, et al., 2016; Sousa et al., 2013; Valdez et al., 2014).

As a result of the link between traditional task-unrelated mind-wandering and learning, educational policy has an enormous potential to be shaped by this and other mind-wandering research. The negative association between task-unrelated thought and text comprehension has been extensively replicated (Franklin, Smallwood, & Schooler, 2011; Mrazek et al., 2017; Pachai et al., 2016; Seli, Wammes, et al., 2016; Smallwood, McSpadden, & Schooler, 2008; Sousa et al., 2013). Additional work suggests that this relationship may be partially explained by mind-wandering’s interference with students’ ability to adaptively adjust their cognitive resources to the current task demands (Mills et al., 2017).

The dynamic fluctuations in mind-wandering found here raise the question of whether students’ schedules can or should be adapted around their cognitive cycles. For example, our findings suggest that early afternoon classes may coincide with peak rates of freely moving thought and stimulus-independence—perhaps making them poor times at which to hold class. However, it is currently unclear what an optimal schedule could be, given that past research has demonstrated learning deficits in early morning classes as well due to factors such as sleepiness (see Valdez et al., 2014).

A contrasting point of view is that mind-wandering is not a hindrance to all educational outcomes, particularly ones that require creativity (Baird et al., 2012; Dijksterhuis & Meurs, 2006; Ellamil, Dobson, Beeman, & Christoff, 2012; Pachai et al., 2016). From this standpoint, school administrators may actually wish to structure class times to take advantage of the benefits of mind-wandering (freely moving thought, in particular), not just avoid the downsides. For example, writing and artistic classes may benefit from being held around midday, when freely moving thought is highest and constraints are lowest. Classes that require a narrower focus of attention (e.g. STEM courses) might be more effective if they are held when freely moving and task-unrelated thought are at their lowest.

It is also important to consider how daily fluctuations in thought influence performance in the workplace. Industrial-organizational research has highlighted the detrimental effects of task-unrelated thought on workplace performance (Dane, 2011;Dust, 2015 ; Hyland et al., 2015) as well as its potentially positive effects (Dust, 2015; Hyland et al., 2015). In driving simulations, task-unrelated thought has been associated variously with poorer speed control (Baldwin et al., 2017; Yanko & Spalek, 2014), slower reaction times (Yanko & Spalek, 2014), and a lack of peripheral awareness (He, Becic, Lee, & McCarley, 2011). Similarly, in real-world correlational studies, this kind of mind-wandering has been associated with risky or aggressive driving patterns (Qu et al., 2015) and responsibility for car accidents (Galéra et al., 2012). Understanding the times of day we are most likely go off-task, have unconstrained thoughts, or be unaware of our surroundings, could be a critical consideration for occupational schedules as well.

Limitations and future directions

Of course, as an early and exploratory study, our work has a number of limitations and we see many of them are prime opportunities for future work. First, we asked people to introspectively report on their thoughts; participants’ introspective abilities have been the subject of much debate in the past (Hurlburt, Alderson-Day, Fernyhough, & Kühn, 2017; Nisbett & Wilson, 1977). However, replication of results across two independent datasets provides some evidence that individuals were responding reliably to the introspective questions. Additionally, extensive training and instructions were included during the training session to compensate for the novelty of the freely moving thought definition. Future work should strive to complement these studies by assessing the phenomenological experience of freely moving thought through its contents over time, as well as its objective signatures through physiological signals (Faber, Bixler, & D’Mello, 2018; Mills, Bixler, Wang, & D’Mello, 2016; Mills & D’Mello, 2015).

Second, we had no experimental control over participants, since the study was conducted in everyday life. This was necessary to maximize ecological validity but means that we had no way of knowing whether participants answered accurately and no way to compel them to answer rapidly. While this provided us with valuable insight into real-world processes, future work should complement naturalistic research (like the present study) with experimental designs that could shed light on processes, mediations, and causal mechanisms.

Third, in Study 1 only 71.4% of all probes were answered on average in the original dataset (80.2% after discarding low responders), leading to some variability in response rates across the hours of the day (see Table 1). This is particularly a problem for hour 23:00, as only 53 participants (fewer than half) answered a single probe during this time period, resulting in a high standard error. As a consequence, it is unclear whether the sharp drop in freely moving thought ratings from 22:00 to 23:00 represents a true effect, a problem made worse by the lack of any 23:00 probes in Study 2. We are nevertheless confident in the pattern of results leading up to 22:00 h, particularly the replicated finding that freely moving thought steadily increased throughout the morning.

Fourth, in order to ensure consistency with the existing literature, 7-point Likert scales were used to measure all three dimensions of thought. While this simplifies the process and allows participants to make quick and intuitive decisions, Likert scales have the disadvantage of being unmoored from common reference points. Put simply, even with verbal anchors, there is no objective meaning of a 4 out of 7 on the scale; as a result, each rating may mean something entirely different to each participant. Once again, we attempted to mitigate this by providing participants with extensive instructions. These instructions even included prompting participants to come up with their own examples of different levels of freely moving thought, ensuring that their ideas were as close as possible both to their cohort’s perceptions and to the experimenters’ expectations.

Fifth, past studies have found evidence that task-unrelated thought may demonstrate fluctuations (Carciofo, Du, Song, & Zhang, 2014; Giambra et al., 1989) similar to those we observed for freely moving thought or stimulus-independent thought. We did not find similar patterns for task-unrelated thought in the present study, but this may be due to significant methodological differences among the studies. Giambra et al. (1989) conducted a sleep-deprivation study intended more to explore natural circadian rhythms of mind-wandering in isolation than fluctuations in real-world environments. Because they used a lab-based task, their participants were judged on whether they were paying attention to a particular narrow assignment they were given. On the other hand, Carciofo et al. (2014) had participants estimate when they were most likely to mind-wander instead of probing them throughout the day; they used a multi-item scale that is related to but different than task-unrelated thought to judge mind-wandering. By contrast, the current study presumably assessed participants’ attention to a variety of tasks performed in their everyday life—and did so while they were engaged in those tasks. Taken together, it is difficult to know whether the results of this study represent a true conflict with the literature or simply a difference between experience-sampling studies and lab-based alternatives.

Finally, it is also possible that the unanswered probes differed systematically from the answered probes. Participants were instructed not to answer probes if doing so would put them in danger (e.g. if they were driving a vehicle). The fact that certain activities were un- or underrepresented may mean that ratings across the three dimensions could be biased in one direction. Of course, given the concern for participant safety, it is impossible to address this concern sufficiently in natural data; instead, experimental paradigms could induce similar settings within controlled environments (e.g. risky driving simulations used by Watson et al., 2016) to empirically test whether and how these underrepresented activities affect the dynamics.

Another important future step beyond the current work is to better understand the mechanisms that may influence the levels of freedom of movement in thought across the day. For example, how do current concerns and other conscious or latent goal pursuits influence our thought patterns, especially when affectively charged? Additionally, it may be fruitful to assess thought patterns in clinical populations that display more fixated thoughts (e.g. individuals with ruminative tendencies). Studies such as these may provide some key insights about the relationship between affect and constraints and how those features influence our freedom of movement in thought throughout our daily lives.

Post-hoc power analyses

The lack of readily available standardized effect size estimates for mixed-effects polynomial models prevented us from determining our desired sample size based on a calculation of required statistical power. We nevertheless conducted post-hoc observed power analyses in order to inform future research about what types of sample sizes are appropriate for such effects. As observed power analyses are only conceptually meaningful when applied to tests of true effects, we conducted them only on significant parameters in order to estimate each study’s ability to detect the fixed effect in question. Although there is not consensus for how to calculate power exactly for multiple-predictor random-effects models (see Brysbaert & Stevens, 2018), we adopted a Monte Carlo simulation approach using the simR package in R (Green & MacLeod, 2015). It should be noted that due to their reliance on simulations, these numbers are not exact; however, setting a seed state before executing the analyses ensures that each analysis is replicable. Our shared code includes a fixed seed to allow readers to completely reproduce our analyses.

In sum, although observed power was lower for Study 1 (which solely focused on freely moving thought), we are encouraged that the patterns for freely moving thought were consistent across both datasets, especially given that observed power was much higher for Study 2. Moreover, based on these analyses, similar research on this topic may want to collect > 165 participants when aiming for > 80% power to detect the smallest effect.