Detecting correlation changes in multivariate time series: A comparison of four non-parametric change point detection methods

Integrating Intra- and Interindividual Phenomena in Psychological Theories

Psychological science is divided into two distinct methodological traditions. One tradition seeks to understand how people function at the individual level, while the other seeks to understand how people differ from each other. Methodologies that have grown out of these traditions typically rely on different sources of data. While both use statistical models to understand the structure of the data, and these models are often similar, Molenaar (2004) showed that results from one type of analysis rarely transfer to the other, unless unrealistic assumptions hold. This raises the question how we may integrate these approaches. In this paper, we argue that formalized theories can be used to connect intra- and interindividual levels of analysis. This connection is indirect, in the sense that the relationship between theory and data is best understood through the intermediate level of phenomena: robust statistical patterns in empirical data. To illustrate this, we introduce a distinction between intra- and interindividual phenomena, and argue that many psychological theories will have implications for both types of phenomena. Formalization provides us with a methodological tool for investigating what kinds of intra- and interindividual phenomena we should expect to find if the theory under consideration were true.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Multivariate Time Series Change-Point Detection with a Novel Pearson-like Scaled Bregman Divergence

Change-point detection is a challenging problem that has a number of applications across various real-world domains. The primary objective of CPD is to identify specific time points where the underlying system undergoes transitions between different states, each characterized by its distinct data distribution. Precise identification of change points in time series omics data can provide insights into the dynamic and temporal characteristics inherent to complex biological systems. Many change-point detection methods have traditionally focused on the direct estimation of data distributions. However, these approaches become unrealistic in high-dimensional data analysis. Density ratio methods have emerged as promising approaches for change-point detection since estimating density ratios is easier than directly estimating individual densities. Nevertheless, the divergence measures used in these methods may suffer from numerical instability during computation. Additionally, the most popular α -relative Pearson divergence cannot measure the dissimilarity between two distributions of data but a mixture of distributions. To overcome the limitations of existing density ratio-based methods, we propose a novel approach called the Pearson-like scaled-Bregman divergence-based (PLsBD) density ratio estimation method for change-point detection. Our theoretical studies derive an analytical expression for the Pearson-like scaled Bregman divergence using a mixture measure. We integrate the PLsBD with a kernel regression model and apply a random sampling strategy to identify change points in both synthetic data and real-world high-dimensional genomics data of Drosophila. Our PLsBD method demonstrates superior performance compared to many other change-point detection methods.

The Duration-Adjusted Reliable Change Index: Defining Clinically Relevant Symptom Changes of Varying Durations

The time period over which relevant symptoms shifts unfold is not uniform across individuals. This article proposes an adaptation of the Reliable Change Index (RCI) to detect symptom changes of varying durations in individual patients' time series: the Duration-Adjusted RCI (DARCI). The DARCI proportionally raises the RCI cut-off to account for its extension over additional time increments, resulting in different DARCI thresholds for different change durations. The method is illustrated with a simulation study of depressive symptom time series with varying degrees of discontinuity and overall mean change, and four empirical case examples from two clinical samples. The results suggest that the DARCI may be particularly useful for identifying symptom shifts that appear relatively abrupt, which can help indicate when a patient is showing significant improvement or deterioration. Its ease of use makes it suitable for application in clinical contexts and a promising method for exploring transitions in psychiatric populations.

Individual-specific change points in circadian rest-activity rhythm and sleep in individuals tapering their antidepressant medication: an actigraphy study

Group-level studies showed associations between depressive symptoms and circadian rhythm elements, though whether these associations replicate at the within-person level remains unclear. We investigated whether changes in circadian rhythm elements (namely, rest-activity rhythm, physical activity, and sleep) occur close to depressive symptom transitions and whether there are differences in the amount and direction of circadian rhythm changes in individuals with and without transitions. We used 4 months of actigraphy data from 34 remitted individuals tapering antidepressants (20 with and 14 without depressive symptom transitions) to assess circadian rhythm variables. Within-person kernel change point analyses were used to detect change points (CPs) and their timing in circadian rhythm variables. In 69% of individuals experiencing transitions, CPs were detected near the time of the transition. No-transition participants had an average of 0.64 CPs per individual, which could not be attributed to other known events, compared to those with transitions, who averaged 1 CP per individual. The direction of change varied between individuals, although some variables showed clear patterns in one direction. Results supported the hypothesis that CPs in circadian rhythm occurred more frequently close to transitions in depression. However, a larger sample is needed to understand which circadian rhythm variables change for whom, and more single-subject research to untangle the meaning of the large individual differences.

Evaluating Covariate Effects on ESM Measurement Model Changes with Latent Markov Factor Analysis: A Three-Step Approach

Invariance of the measurement model (MM) between subjects and within subjects over time is a prerequisite for drawing valid inferences when studying dynamics of psychological factors in intensive longitudinal data. To conveniently evaluate this invariance, latent Markov factor analysis (LMFA) was proposed. LMFA combines a latent Markov model with mixture factor analysis: The Markov model captures changes in MMs over time by clustering subjects' observations into a few states and state-specific factor analyses reveal what the MMs look like. However, to estimate the model, Vogelsmeier, Vermunt, van Roekel, and De Roover (2019) introduced a one-step (full information maximum likelihood; FIML) approach that is counterintuitive for applied researchers and entails cumbersome model selection procedures in the presence of many covariates. In this paper, we simplify the complex LMFA estimation and facilitate the exploration of covariate effects on state memberships by splitting the estimation in three intuitive steps: (1) obtain states with mixture factor analysis while treating repeated measures as independent, (2) assign observations to the states, and (3) use these states in a discrete- or continuous-time latent Markov model taking into account classification errors. A real data example demonstrates the empirical value.

: An R Package for performing kernel change point detection on the running statistics of multivariate time series

In many scientific disciplines, researchers are interested in discovering when complex systems such as stock markets, the weather or the human body display abrupt changes. Essentially, this often comes down to detecting whether a multivariate time series contains abrupt changes in one or more statistics, such as means, variances or pairwise correlations. To assist researchers in this endeavor, this paper presents the package for performing kernel change point (KCP) detection on user-selected running statistics of multivariate time series. The running statistics are extracted by sliding a window across the time series and computing the value of the statistic(s) of interest in each window. Next, the similarities of the running values are assessed using a Gaussian kernel, and change points that segment the time series into maximally homogeneous phases are located by minimizing a within-phase variance criterion. To decide on the number of change points, a combination of a permutation-based significance test and a grid search is provided. stands out among the variety of change point detection packages available in because it can be easily adapted to uncover changes in any user-selected statistic without imposing any distribution on the data. To exhibit the usefulness of the package, two empirical examples are provided pertaining to two types of physiological data.

Evidence and theory for lower rates of depression in larger US urban areas

It is commonly assumed that cities are detrimental to mental health. However, the evidence remains inconsistent and at most, makes the case for differences between rural and urban environments as a whole. Here, we propose a model of depression driven by an individual's accumulated experience mediated by social networks. The connection between observed systematic variations in socioeconomic networks and built environments with city size provides a link between urbanization and mental health. Surprisingly, this model predicts lower depression rates in larger cities. We confirm this prediction for US cities using four independent datasets. These results are consistent with other behaviors associated with denser socioeconomic networks and suggest that larger cities provide a buffer against depression. This approach introduces a systematic framework for conceptualizing and modeling mental health in complex physical and social networks, producing testable predictions for environmental and social determinants of mental health also applicable to other psychopathologies.

Early warning signals and critical transitions in psychopathology: challenges and recommendations

Empirical evidence is mounting that monitoring momentary experiences for the presence of early warning signals (EWS) may allow for personalized predictions of meaningful symptom shifts in psychopathology. Studies aiming to detect EWS require intensive longitudinal measurement designs that center on individuals undergoing change. We recommend that researchers (1) define criteria for relevant symptom shifts a priori to allow specific hypothesis testing, (2) balance the observation period length and high-frequency measurements with participant burden by testing ambitious designs with pilot studies, and (3) choose variables that are meaningful to their patient group and facilitate replication by others. Thoroughly considered designs are necessary to assess the promise of EWS as a clinical tool to detect, prevent, or encourage impending symptom changes in psychopathology.

SpaTemHTP: A Data Analysis Pipeline for Efficient Processing and Utilization of Temporal High-Throughput Phenotyping Data

The rapid development of phenotyping technologies over the last years gave the opportunity to study plant development over time. The treatment of the massive amount of data collected by high-throughput phenotyping (HTP) platforms is however an important challenge for the plant science community. An important issue is to accurately estimate, over time, the genotypic component of plant phenotype. In outdoor and field-based HTP platforms, phenotype measurements can be substantially affected by data-generation inaccuracies or failures, leading to erroneous or missing data. To solve that problem, we developed an analytical pipeline composed of three modules: detection of outliers, imputation of missing values, and mixed-model genotype adjusted means computation with spatial adjustment. The pipeline was tested on three different traits (3D leaf area, projected leaf area, and plant height), in two crops (chickpea, sorghum), measured during two seasons. Using real-data analyses and simulations, we showed that the sequential application of the three pipeline steps was particularly useful to estimate smooth genotype growth curves from raw data containing a large amount of noise, a situation that is potentially frequent in data generated on outdoor HTP platforms. The procedure we propose can handle up to 50% of missing values. It is also robust to data contamination rates between 20 and 30% of the data. The pipeline was further extended to model the genotype time series data. A change-point analysis allowed the determination of growth phases and the optimal timing where genotypic differences were the largest. The estimated genotypic values were used to cluster the genotypes during the optimal growth phase. Through a two-way analysis of variance (ANOVA), clusters were found to be consistently defined throughout the growth duration. Therefore, we could show, on a wide range of scenarios, that the pipeline facilitated efficient extraction of useful information from outdoor HTP platform data. High-quality plant growth time series data is also provided to support breeding decisions. The R code of the pipeline is available at https://github.com/ICRISAT-GEMS/SpaTemHTP.

Inspecting Gradual and Abrupt Changes in Emotion Dynamics With the Time-Varying Change Point Autoregressive Model

Abstract. Recent studies have shown that emotion dynamics such as inertia (i.e., autocorrelation) can change over time. Importantly, current methods can only detect either gradual or abrupt changes in inertia. This means that researchers have to choose a priori whether they expect the change in inertia to be gradual or abrupt. This will leave researchers in the dark regarding when and how the change in inertia occurred. Therefore in this article, we use a new model: the time-varying change point autoregressive (TVCP-AR) model. The TVCP-AR model can detect both gradual and abrupt changes in emotion dynamics. More specifically, we show that the inertia of positive affect and negative affect measured in one individual differs qualitatively in how it changes over time. Whereas the inertia of positive affect increased only gradually over time, negative affect changed both in a gradual and abrupt fashion over time. This illustrates the necessity of being able to model both gradual and abrupt changes in order to detect meaningful quantitative and qualitative differences in temporal emotion dynamics.

Detecting long-lived autodependency changes in a multivariate system via change point detection and regime switching models

Long-lived simultaneous changes in the autodependency of dynamic system variables characterize crucial events as epileptic seizures and volcanic eruptions and are expected to precede psychiatric conditions. To understand and predict such phenomena, methods are needed that detect such changes in multivariate time series. We put forward two methods: First, we propose KCP-AR, a novel adaptation of the general-purpose KCP (Kernel Change Point) method. Whereas KCP is implemented on the raw data and does not shed light on which parameter changed, KCP-AR is applied to the running autocorrelations, allowing to focus on changes in this parameter. Second, we revisit the regime switching AR(1) approach and propose to fit models wherein only the parameters capturing autodependency differ across the regimes. We perform a simulation study comparing both methods: KCP-AR outperforms regime switching AR(1) when variables are uncorrelated, while the latter is more reliable when multicolinearity is severe. Regime switching AR(1), however, may yield recurrent switches even when the change is long-lived. We discuss an application to psychopathology data where we investigate whether emotional inertia -the autodependency of affective states- changes before a relapse into depression.

Affective family interactions and their associations with adolescent depression: A dynamic network approach

The prevalence of depression rises steeply during adolescence. Family processes have been identified as one of the important factors that contribute to affect (dys)regulation during adolescence. In this study, we explored the affect expressed by mothers, fathers, and adolescents during a problem-solving interaction and investigated whether the patterns of the affective interactions differed between families with depressed adolescents and families with nondepressed adolescents. A network approach was used to depict the frequencies of different affects, concurrent expressions of affect, and the temporal sequencing of affective behaviors among family members. The findings show that families of depressed adolescents express more anger than families of nondepressed adolescents during the interaction. These expressions of anger co-occur and interact across time more often in families with a depressed adolescent than in other families, creating a more self-sustaining network of angry negative affect in depressed families. Moreover, parents' angry and adolescents' dysphoric affect follow each other more often in depressed families. Taken together, these patterns reveal a particular family dynamic that may contribute to vulnerability to, or maintenance of, adolescent depressive disorders. Our findings underline the importance of studying affective family interactions to understand adolescent depression.

Testing for the Presence of Correlation Changes in a Multivariate Time Series: A Permutation Based Approach

Detecting abrupt correlation changes in multivariate time series is crucial in many application fields such as signal processing, functional neuroimaging, climate studies, and financial analysis. To detect such changes, several promising correlation change tests exist, but they may suffer from severe loss of power when there is actually more than one change point underlying the data. To deal with this drawback, we propose a permutation based significance test for Kernel Change Point (KCP) detection on the running correlations. Given a requested number of change points K, KCP divides the time series into K + 1 phases by minimizing the within-phase variance. The new permutation test looks at how the average within-phase variance decreases when K increases and compares this to the results for permuted data. The results of an extensive simulation study and applications to several real data sets show that, depending on the setting, the new test performs either at par or better than the state-of-the art significance tests for detecting the presence of correlation changes, implying that its use can be generally recommended.