Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

Moulder, Robert; Мартынова, Е. А.; Boker, Steven M.

doi:10.1080/00273171.2021.1994848

Cited by 6 publications

(4 citation statements)

References 86 publications

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“…With modern technology, everyday thoughts, emotions, and behaviors of the person have never been more accessible. As psychologists begin to emphasize intraindividual processes over interindividual predictions, statistical models that answer questions about the dynamics of systems are needed (Epskamp et al, 2018b;e.g., Gates & Molenaar, 2012;Moulder, Martynova, & Boker, 2021;Sterba & Bauer, 2010). The present work provides one statistical tool to understand whether intraindividual dynamics can be reasonably aggregated into a single interindividual structure and another tool to determine possible sub-aggregations when they cannot.…”

Section: Discussionmentioning

confidence: 92%

Towards a psychology of individuals: the ergodicity information index and a bottom-up approach for finding generalizations

Golino¹,

Christensen²,

Nesselroade³

2022

Preprint

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In the last half of the 20th century, psychology and neuroscience have experienced a renewed interest in intraindividual variation. To date, there are few quantitative methods to evaluate whether a population structure (between-person) is likely to hold for individual people. We present a network information theoretic approach to evaluate the extent to which a system possesses the ergodic property. We introduce a new metric, the ergodicity information index (EII), that can inform whether a set of multivariate time series (or a set of intensive longitudinal measures) should be represented as multiple individual structures or as a single population structure. The EII index quantifies the amount of information lost by representing all individuals with a single population structure. If the individuals don't have a similar structure, representing them with a single population network leads to a loss of information. The EII index value will be higher than in cases where all individuals have a similar structure. A Monte-Carlo simulation is implemented to test the EII index, and the results show that the new index has a 94% accuracy in differentiating data in which all individuals have a similar structure vs. data in which the individuals don't have a similar structure. The paper also presents two new techniques designed to help applied researchers to analyze data when the ergodicity property does not hold. The EII bootstrap test obtains a sampling distribution of EII values as if all participants in the data have the population network structure and compare this null distribution to the empirical EII value. Significant differences indicate that the empirical data cannot be expected to be generated from an ergodic process, and the population structure is not sufficient to describe all individuals. The Domenico clustering method estimates the Von Neumann entropy of two networks and computes their Jensen-Shannon Distance (JSD). Then, a complete-linkage agglomerative hierarchical clustering method is applied to the JSD, and the clustering partitioning is obtained via modularization maximization. The Domenico clustering method allows the discovery of groups of individuals with a similar structure. Finally, two empirical examples are shown, one using data from an intensive longitudinal experience sampling study examining Big Five personality measured by the Big Five Inventory-2, and the other using resting state neuroimaging data taken from a study examining creativity which used the 268-node Shen brain atlas. Starting with personality, the bootstrap EII test was significant, suggesting that the BFI-2 data were nonergodic. Following up on the bootstrap EII test, the information clustering was applied, and the single cluster test was performed. The single cluster test suggested that the empirical networks had significantly greater JSD values than the random networks meaning that the single cluster detected was not meaningful, and each individual in the sample is unique. The brain networks had a significant bootstrap EII test and significantly larger JSD values than random networks. These results, in line with the personality data, suggest that (resting state) brain networks are not ergodic, and no meaningful groups can be formed (i.e., each individual is unique). In sum, the personality and (resting state) brain networks do not possess ergodicity and therefore lose information when data are aggregated into a single population.

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Section: Discussionmentioning

confidence: 92%

Towards a psychology of individuals: the ergodicity information index and a bottom-up approach for finding generalizations

Golino¹,

Christensen²,

Nesselroade³

2022

Preprint

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show abstract

“…HAVOK analysis was applied to the preprocessed time series through the havok() R package (Moulder et al, 2021). 7,021 HAVOK models were Ąt in the stackmax (number of shift-stacked rows in the Hankel matrix) and r (model degree/ truncation parameter)…”

Section: Resultsmentioning

confidence: 99%

“…For a more extensive tutorial than we can supply here, please refer toMoulder, Martynova, and Boker (2021).…”

mentioning

confidence: 99%

Playing HAVOK on the Chaos Caused by Internet Trolls

Мартынова

Golino

Boker

2023

Preprint

Self Cite

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Trump supporting Twitter posting activity from right-wing Russian trolls active during the 2016 United States presidential election was analyzed at multiple timescales using a recently developed procedure for separating linear and nonlinear components of time series. Trump supporting topics were extracted with DynEGA (Dynamic Exploratory Graph Analysis) and analyzed with Hankel Alternative View of Koopman (HAVOK) procedure. HAVOK is an exploratory and predictive technique that extracts a linear model for the time series and a corresponding nonlinear time series that is used as a forcing term for the linear model. Together, this forced linear model can produce surprisingly accurate reconstructions of nonlinear and chaotic dynamics. Using the R package havok, Russian troll data yielded well-fitting models at several timescales, not producing well-fitting models at others, suggesting that only a few timescales were important for representing the dynamics of the troll factory. We identified system features that were timescale-universal versus timescale-specific. Timescale-universal features included cycles inherent to troll factory governance, which identified their work-day and work-week organization, later confirmed from published insider interviews. Cycles were captured by eigen-vector basis components resembling Fourier modes, rather than Legendre polynomials typical for HAVOK. This may be interpreted as the troll factory having intrinsic dynamics that are highly coupled to nearly stationary cycles. Forcing terms were timescale-specific. They represented external events that precipitated major changes in the time series and aligned with major events during the political campaign. HAVOK models specified interactions between the discovered components allowing to reverse-engineer the operation of Russian troll factory. Steps and decision points in the HAVOK analysis are presented and the results are described in detail.

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“…• Time series analysis (TSA) decomposes an event into trend, cycle, period, and unstable factors. It emphasizes the extraction of relevant event features and the analysis of its change process and development mode through continuous observation of a region within a certain period of time [34].…”

Section: Fusion Of Methodsmentioning

confidence: 99%

Tight or Loose: Analysis of the Organization Cognition Process of Epidemic Risk and Policy Selection

Fan,

Zhuang,

Qian

2024

Sustainability

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In the context of Disease X risks, how governments and public health authorities make policy choices in response to potential epidemics has become a topic of increasing concern. The tightness of epidemic prevention policies is related to the effectiveness of the implementation of measures, while the organizational cognition of epidemic risks is related to the rationality of policy choices. During the three years of COVID-19, the Chinese government constantly adjusted the tightness of its prevention policies as awareness of the epidemic risk improved. Therefore, based on the epidemic risk organizational cognition model, the key nodes that affect the tightness of epidemic prevention policies can be explored to find the organizational behavior rules behind the selection of prevention policies. Firstly, through observing the adjustments made to the Chinese government’s prevention strategies during the epidemic, a time-series cross-case comparative analysis reveals how policy tightness shifted from stringent to lenient. This shift coincided with the organizational cognition of epidemic risk evolving from vague to clear. Secondly, by building the “knowledge-cognition” coordinate system to draw the organizational cognition spiral of epidemic risk, it is clear that the changes in the tightness of the prevention policies mainly came from the internalization and externalization of knowledge such as epidemic risk characteristics to promote the level of organizational cognition, which is manifested as expansion and deepening. Thirdly, the node changes in the interaction between organizational cognition development and policy choice proved that different stages of the epidemic had diverse environmental parameters. Moreover, as the epidemic nears its end, the focus of policy tightness is shifting from policy objectives to policy implementation around governance tools. The results indicate that organizational cognition of epidemic risk exhibits significant stages and periodicity. Additionally, epidemic risk characteristics, environmental coupling, and governance tools are crucial factors in determining the tightness of epidemic prevention policies.

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Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

Cited by 6 publications

References 86 publications

Towards a psychology of individuals: the ergodicity information index and a bottom-up approach for finding generalizations

Towards a psychology of individuals: the ergodicity information index and a bottom-up approach for finding generalizations

Playing HAVOK on the Chaos Caused by Internet Trolls

Tight or Loose: Analysis of the Organization Cognition Process of Epidemic Risk and Policy Selection

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