Complexity in psychological self-ratings: implications for research and practice

Publicly available EMA data from the study “Critical Slowing Down as a Personalized Early Warning Signal for Depression” were analyzed [63, 64]. The dataset contains 1476 self-ratings over 239 consecutive days from a single individual. Data were collected during a double-blind experiment in which the participant reduced his dosage of anti-depressant medication. Twenty-nine items on momentary states of affect, symptoms, self-esteem, and physical sensations were rated on Likert and bipolar scales (ranging from 1 to 7 or from − 3 to + 3; items in Table 2). This was done multiple times per day during a baseline period, a period of dosage reduction, and after the dosage reduction. On average, the participant completed 6.2 (SD = 1.9) assessments per day. In addition, there were daily measures in the morning and evening regarding sleep and evaluation of the day, respectively. For a complete description of the dataset, see [63]. In the present study, we analyzed the twenty-nine items on momentary states. The time series of these items have 1476 observations per item. In total, 103 observations were missing, which is less than 1% of all observations (0.24%). The present dataset was chosen because of the long time series, which are necessary for several analysis techniques employed.

The time series were analyzed for markers of complexity using the methods and tests listed in Table 1. This was done twice: once for the full measurement period and once for the “baseline period” only, consisting of 292 assessments that were completed when the participant was not yet tapering medication. We analyzed the baseline period separately in order to examine to what extent the complexity markers were present when clinical change (relapse into depression) was presumably absent. Data analysis of both measurement periods was done with missing data excluded and with missing data imputed by a multivariate imputation algorithm using chained equations [65]. Results were highly similar, likely because of the low number of missing values. We report here on the analysis with missing observations excluded. Each marker was calculated for each time series separately. When a statistical test was used, we corrected for multiple testing with Bonferroni correction by dividing the conventional alpha level of .05 by the amount of items tested and rounding to 3 decimals. A result was therefore considered significant when p < .002. All analyses were performed in R [66]. The materials to reproduce the present analysis are available at the open science framework (https://​osf.​io/​nca2u/​). We elaborate on the specific tests in the “Results” section.

Phase transitions can be reflected in time series data as regime shifts: distributional changes in the time series including changes in mean and variance. Statistically, this leads to non-stationarity. We tested the hypothesis that time series could be seen as stationary around a level using the KPSS test as available in the R-package tseries [70]. The alternative hypothesis of the test is the presence of a unit root: a systematic unpredictable pattern, indicating non-stationarity. Results are presented in Table 2. Non-stationarity was found in many items when tested over the whole measurement period and in few items for the baseline period. Additionally, we estimated the number of regime shifts with a change point analysis, specifically the e.divisive algorithm, available in the R-package epc [71], which identifies significant changes in the distribution of data points over time. E.divisive compares all possible data segments and tests significance differences using a permutation test. The results show that many items have multiple change points, especially when the full measurement period is considered. In the baseline period, one can see largely converging results from the non-stationarity test and the change point analysis.

Visual inspection of the results from the change point analysis suggests a relation between regime shifts in the time series of some items and the transition towards a depressive episode that the participant experienced. This is clearly illustrated for the item “I feel down” (Fig. 4) that was also found to be non-stationary (Table 1). One can see that the transition towards depression (Fig. 4; red line) is preceded by a period of instability in the time series, in which the item “I feel down” flickers between two regimes, one associated with lower scores and one with higher scores. After the transition towards the depressive episode, the time series settles in the regime with higher scores. Notably, the time series of the other items sometimes show regime shifts that seem related to the transition towards depression (as in Fig. 4), but there are also many regime shifts during presumably more stable periods in the participant’s mental state (figures of change points for all items are available online at the open science framework).

Sensitive dependence on initial conditions means that an extremely small difference between two trajectories at present can lead to dramatically large differences in the future, i.e., a divergence of trajectories. This divergence is the result of nonlinearity, a property that is typical for complex systems. As a consequence of sensitive dependence on initial conditions, complex systems tend to produce trajectories that are predictable only on the short term. Predictability can therefore be used to distinguish between different types of systems. Random systems have no predictability at all, simple deterministic systems (e.g., a sine wave) are perfectly predictable both short and long term. Complex systems lie in between these extremes: the predictability of their trajectory quickly decays over time.

First, the presence of both short- and long-term memory has methodological implications. Widely applied statistical time series models of psychological dynamics, i.e., autoregressive (AR) models, do often not account for long-term memory [14, 26]. In these models, the current value of a variable is typically predicted by values in the near past (usually lag 1, or lag 2; e.g., [68]), but not in the distant past. Not taking into account long-range temporal correlations can “completely invalidate statistical inference” [92]. However, taking these long-range temporal correlations into account in a statistical model is far from straightforward. In the current study, we found for many items significant partial autocorrelations in as much as 20 different lags. In an AR model, these would be modeled as 20 independent, additive processes that influence the current state of the system. In other areas of psychological science, there is much debate about whether this is a sensible model to describe a time series [45, 93‐95]. Proponents of AR models argue that the different autocorrelations represent distinct additive causal processes [95]. Complexity scientists argue that they do not, and propose the presence of long-range correlations to be a consequence of self-organized interactions between interdependent (i.e., non-additive) causal processes at different temporal scales [96]. The latter argument is supported by the fact that long-range correlations are ubiquitous in nature, even when distinct additive causal processes are clearly absent (e.g., self-organization in a pile of sand [41]). Moreover, data with non-stationary autocorrelation functions, as we observed, cannot be generated by the most flexible AR model (i.e., the autoregressive fractally integrated moving average model [97]), but can be generated by models that feature interaction across scales (i.e., cascade models [45]). Thus, following a complex systems perspective that embraces self-organization as the causal mechanism, statistical models of time series can only be used descriptively and not as formal models of the underlying causal processes (see also [98]).

Vector autoregressive (VAR) models are time series models that include multiple variables that may predict themselves and each other at specific lags (often restricted to lag 1 in psychopathology research). VAR models are used to examine Granger causality [99]. Granger causality entails that if a variable X at one time point predicts a variable Y at a future time point beyond the autoregressive effect of Y (how Y predicts itself), X can be said to be Granger causal for Y. Although researchers using VAR models are careful in interpreting their models in causal terms, the general idea of these models is that they at least can give a hint of possible causal relations. Accordingly, variables that are Granger causal for many other variables are suggested as targets for treatment (e.g., [68]). This reasoning, however, is problematic under conditions of complexity. Due to the presence of short- and long-term memory, time series are not stochastic beyond what is typically modeled by the VAR model, meaning that Granger causality does not apply [99]. Sugihara et al. [100] illustrate that the (lagged) correlations between variables in a complex (eco)system are indeed bad indicators for causality. Two variables that have a stable causal connection in a complex system may exhibit non-stationary correlation with each other, even to the point that the correlation coefficient switch signs [100]. In a simulation study on psychological dynamics, Haslbeck and Ryan [101] found that a VAR model cannot retrieve the complex systems model that generated the data. Sugihara et al. [100] propose convergent cross mapping as a possible alternative for Granger causality. Also, recurrence-based analysis, which requires no assumptions concerning the structure of the data, may be a promising approach to investigate the dynamics of EMA data [89, 102, 103]. Future research should further examine these techniques for psychological self-ratings.

Second, complex systems exhibit phase transitions, which lead to regime shifts and thus non-stationarity in time series data. While regime shifts are generally undesirable in statistical approaches to psychological dynamics [26], they are an important research avenue in a complex systems approach. In the dynamic research strategy outlined by Thelen and Ulrich [23], phase transitions form the starting point for the study of developmental and also clinical change.

Third, complex systems show sensitive dependence on initial conditions, which implies that psychological dynamics are predictable in the short term, but not in the long term. For clinical science, this means that long-term prediction of individual trajectories may be fundamentally impossible. Instead, researchers should aim at short-term prediction and be careful in forecasting further in the future as predictions will become increasingly unreliable. Short-term prediction is a promising future direction for intervention science, as it may enable just-in-time interventions (e.g., [110]). It should be noted, however, that advancements are made in deriving the governing equations of complex systems from time series data, in which case long-term prediction would in theory become possible (e.g., [111]). Future research could explore the possibility to derive such equations from EMA data.

If we accept the three markers and their meaning in complex systems theories as fundamental aspects of psychopathology and clinical change, this has several implications for clinical practice and public health. Note that, in contrast to the scientific implications given above, these implications are more on a conceptual level, rather than a data level, and therefore arguably more speculative. Our primary aim is to illustrate how the clinical implications of a complex systems approach, as we and others have proposed elsewhere [1, 2, 90, 91], relate to the three characteristics that we examined.

First, our findings regarding memory support the assumption that psychopathology emerges from self-organized interactions between processes at different temporal scales [90]. Current psychopathology is then the result of a unique life-span history of interaction events, which can explain why psychopathology is highly individualized [4, 14]. For clinical practice, this implies that classification is fundamentally limited for clinical case formulation (although it may fulfill a practical function). Instead, personalized case conceptualization should be preferred [12].

Second, our findings regarding regime shifts support the idea that clinical change represents a phase transition from one attractor to another (e.g., a transition into a depressive episode). Therapeutic change is then expected to be discontinuous and irregular rather than continuous and gradual. Also, this means that dose-response relations in psychopathology will often be disproportional [112]: when a patient is in an entrenched psychopathological attractor, interventions will have very little effect, but if a patient is close to a tipping point, small interventions can have enormous effects. The hypothesis that treatment is increasingly effective during destabilization periods is an important avenue for future research. The generic principles of therapeutic change by Schiepek et al. [2] and the network destabilization and transition model by Hayes et al. [1] provide two (related) process-oriented frameworks for how clinicians may support phase transitions towards clinical improvement in psychotherapy. Central to these approaches is that treatment does not follow a strict protocol, but is personalized to the dynamic state of the patient (e.g., in a stable attractor or a destabilization period).

Third, as exemplified by sensitive dependence on initial conditions, we expect clinical change processes to follow complex individual pathways that are very hard to predict based on baseline characteristics, rather than standard tracks [61]. On the individual level, clinical change processes are highly irregular and fluctuating, as comes apparent when enough measurements are taken. Too few measurements (e.g., only pre and post) can then be misleading, and frequent process monitoring (e.g., with daily self-ratings) is essential for a valid measure of the change processes [113] (for an overview of all scientific and clinical implications, see Table 3).

Last, we propose two (complementary) directions for future research: a nomothetic and an idiographic approach. First, the nomothetic approach to psychopathology research should aim at identifying and understanding general properties of clinical change based on the principles of complex systems (e.g., phase transitions). These general principles govern laws of within-system changes and thus cannot be derived from traditional group-level research but by drawing generalizations across cases, possibly in a multi-level framework ([9]; e.g., [52]). Research questions in this approach are as follows: how is destabilization related to clinical change? Can we predict phase transitions? Are interventions more effective during periods of destabilization?

Second, we propose an idiographic approach which, informed by nomothetic research, should aim at studying the manifestation of these general principles in single individuals, thereby providing individualized and contextualized content. Research questions in this approach are as follows: what does the psychopathological state of a patient entail? What feedback loops might play a role in maintaining this state? What might be possible control parameters that drive a client to its tipping point towards a more healthy psychological state? Such an idiographic approach, informed by general principles, provides an excellent starting point for applied clinical research which may directly inform clinical decision-making (for steps in this direction, see, e.g., [108, 110, 113]).