Exploring the Dynamics of Dyadic Interactions via Hierarchical Segmentation

In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to describe the steps and properties of HS. We then use empirical data on daily affect from one couple to illustrate the use of HS for describing the affective dynamics of the dyad. First, we partition the data into three periods that represent different affective states and show different dynamics between both individuals’ affect. We then examine the synchrony between both individuals’ affective states and identify different patterns of coherence across the periods. Finally, we discuss the possibilities of using results from HS to construct confirmatory dynamic models with multiple change points or regime-specific dynamics.     

Detection of long‐range dependence and estimation of fractal exponents through ARFIMA modelling

We evaluate the performance of autoregressive, fractionally integrated, moving average (ARFIMA) modelling for detecting long‐range dependence and estimating fractal exponents. More specifically, we test the procedure proposed by Wagenmakers, Farrell, and Ratcliff , and compare the results obtained with the Akaike information criterion (AIC) and the Bayes information criterion (BIC). The present studies show that ARFIMA modelling is able to adequately detect long‐range dependence in simulated fractal series. Conversely, this method tends to produce a non‐negligible rate of false detections in pure autoregressive and moving average (ARMA) series. Generally, ARFIMA modelling has a bias favouring the detection of long‐range dependence. AIC and BIC gave dissimilar results, due to the different weights attributed by the two criteria to accuracy and parsimony. Finally, ARFIMA modelling provides good estimates of fractal exponents, and could adequately complement classical methods, such as spectral analysis, detrended fluctuation analysis or rescaled range analysis.     

单维测验合成信度元分析

元分析是根据现有研究对感兴趣的主题得出比较准确和有代表性结论的一种重要方法,在心理、教育、管理、医学等社会科学研究中得到广泛应用。信度是衡量测验质量的重要指标,用合成信度能比较准确的估计测验信度。未见有文献提供合成信度元分析方法。本研究在比较对参数进行元分析的三种模型优劣的基础上,在变化系数模型下推出合成信度元分析点估计及区间估计的方法;以区间覆盖率为衡量指标,模拟研究表明本研究提出的合成信度元分析区间估计的方法得当;举例说明如何对单维测验的合成信度进行元分析。     

The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model

A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models.     

Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models

Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.     

Bayesian Estimation of Random Coefficient Dynamic Factor Models

Dynamic factor models (DFMs) have typically been applied to multivariate time series data collected from a single unit of study, such as a single individual or dyad. The goal of DFMs application is to capture dynamics of multivariate systems. When multiple units are available, however, DFMs are not suited to capture variations in dynamics across units. The aims of this study are (a) to propose a random coefficient DFM (RC-DFM) to statistically model variations of dynamics across multiple units using the Bayesian method, (b) to illustrate the use of the proposed procedure by applying RC-DFMs to affect data collected from multiple dyads in romantic relationships, and (c) to evaluate the performance of the RC-DFMs with Bayesian estimation through simulation analyses. The results from the simulation analyses show that the Bayesian estimation of RC-DFMs works well in recovering parameters including both fixed and random effects. A number of practical considerations are provided to guide future research on using Bayesian methods for estimating multivariate time series from multiple units.     

Invariance Properties for General Diagnostic Classification Models

In item response theory (IRT), the invariance property states that item parameter estimates are independent of the examinee sample, and examinee ability estimates are independent of the test items. While this property has long been established and understood by the measurement community for IRT models, the same cannot be said for diagnostic classification models (DCMs). DCMs are a newer class of psychometric models that are designed to classify examinees according to levels of categorical latent traits. We examined the invariance property for general DCMs using the log-linear cognitive diagnosis model (LCDM) framework. We conducted a simulation study to examine the degree to which theoretical invariance of LCDM classifications and item parameter estimates can be observed under various sample and test characteristics. Results illustrated that LCDM classifications and item parameter estimates show clear invariance when adequate model data fit is present. To demonstrate the implications of this important property, we conducted additional analyses to show that using pre-calibrated tests to classify examinees provided consistent classifications across calibration samples with varying mastery profile distributions and across tests with varying difficulties.     

Executive Function as an Interaction-Dominant Process

Traditional theories of psychology define the cognitive system as composed of insular, encapsulated components, controlled by a central executive. An alternative hypothesis suggests that cognitive control arises from the complex interaction among temporal scales of activity within the system. We examined the hand motions of preschool-age participants gathered during an executive-function task, card sorting, for evidence of multiplicative interactions across temporal scales. The time series of hand motions were submitted to iterated amplitude adjusted Fourier transformation (IAAFT), a surrogate data analysis technique that removes nonlinear, multiscale dependencies while preserving the linear structure of the time series. We found that removing multiscale effects via IAAFT led to a significant change in the width of the multifractal spectrum, an indicator of multiplicative interactions. The results suggest that cognitive control may arise from the interactions among temporal scales of activity within the system rather than as the result of a central executive.     

Idiographic network analysis of discrete mood states prior to treatment

Idiographic network models based on time‐series data have received recent attention for their ability to model relationships among symptoms and behaviours as they unfold in time within a single individual (cf. Epskamp, Borsboom, & Fried, 2018; Fisher, Medaglia, & Jeronimus, 2018). Rather than examine the correlational relationships between variables in a sample of individuals, an idiographic network examines correlations within a single person, averaged over many time points. Because the approach averages over time, the data must be stationary (i.e. relatively consistent over time). If individuals experience varying states over time—different mixtures of symptoms and behaviours in one moment or another—then averaging over categorically different moments may undermine model accuracy. Fisher and Bosley (2019) address these concerns via the application of Gaussian finite mixture modelling to identify latent classes of time points in intraindividual time‐series data from a sample of adults with major depressive disorder and/or generalised anxiety disorder (n = 45). The present paper outlines an extension of this work, wherein network analysis is used to model within‐class covariation of symptoms. To illustrate this approach, network models were constructed for each intraindividual class identified by Fisher and Bosley (137 networks across the 45 participants, mean classes/person = ~3, range = 2–4 classes/person). We examine the relative consistency in symptom organisation between each individual's multiple mood state networks and assess emergent group‐level patterns. We highlight opportunities for enhanced treatment personalisation and review nomothetic patterns relevant to transdiagnostic conceptualisations of psychopathology. We address opportunities for integrating this approach into clinical practice and outline potential shortcomings.     

Impact of series length on statistical precision and sensitivity of autocorrelation assessment in human locomotion

Long-range autocorrelations (LRA) are a robust feature of rhythmic movements, which may provide important information about neural control and potentially constitute a powerful marker of dysfunction. A clear difficulty associated with the assessment of LRA is that it requires a large number of cycles to generate reliable results. Here we investigate how series length impacts the reliability of LRA assessment. A total of 94 time series extracted from walking or cycling tasks were re-assessed with series length varying from 64 to 512 data points. LRA were assessed using an approach combining the rescaled range analysis or the detrended fluctuation analysis (Hurst exponent, H), along with the shape of the power spectral density (α exponent). The statistical precision was defined as the ability to obtain estimates for H and α that are consistent with their theoretical relationship, irrespective of the series length. The sensitivity consisted of testing whether significant differences between experimental conditions found in the original studies when considering 512 data points persisted with shorter series. We also investigate the use of evenly-spaced diffusion plots as a methodological improvement of original version of methods for short series. Our results show that the reliable assessment of LRA requires 512 data points, or no shorter than 256 data points provided that more robust methods are considered such as the evenly-spaced algorithms. Such series can be reasonably obtained in clinical populations with moderate, or even more severe, gait impairments and open the perspective to extend the use of LRA assessment as a marker of gait stability applicable to a broad range of locomotor disorders.     

The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

Stochastic analysis of the duration of the speaker role in psychotherapy

An analysis has been undertaken of the stochastic behavior of the time series which defines the duration of utterances exchanged by patients and therapists in six recorded sessions of psychotherapy. Each series followed a Box-Jenkins time series model of order (1, 0, 0): that is, each behaved as a first-order autoregressive process, sensitive to the prior state of the system. The confidences associated with the parameters of the autoregressive models were very high. In addition, the histograms of length of each utterance indicated an underlying Poisson model for the emergence of speech. The parameters of the Poisson and autoregressive models varied with each patient/therapist pair. Signatures for the process dynamics of the speaker-role variable were obtained. The two analyses suggest fundamental structures within the psychotherapeutic dialogue. The Box-Jenkins results provide a global summary of the inner structure of the series and its progression, while the Poisson results describe its instantaneous behavior. This work is offered as a part of new efforts to apply scientific and mathematical methods to the psychotherapeutic domain.     

A Limited Information Estimator for Dynamic Factor Models

Structural equation modeling (SEM) is an increasingly popular method for examining multivariate time series data. As in cross-sectional data analysis, structural misspecification of time series models is inevitable, and further complicated by the fact that errors occur in both the time series and measurement components of the model. In this article, we introduce a new limited information estimator and local fit diagnostic for dynamic factor models within the SEM framework. We demonstrate the implementation of this estimator and examine its performance under both correct and incorrect model specifications via a small simulation study. The estimates from this estimator are compared to those from the most common system-wide estimators and are found to be more robust to the structural misspecifications considered.     

Capturing Context-Related Change in Emotional Dynamics via Fixed Moderated Time Series Analysis

Much of recent affect research relies on intensive longitudinal studies to assess daily emotional experiences. The resulting data are analyzed with dynamic models to capture regulatory processes involved in emotional functioning. Daily contexts, however, are commonly ignored. This may not only result in biased parameter estimates and wrong conclusions, but also ignores the opportunity to investigate contextual effects on emotional dynamics. With fixed moderated time series analysis, we present an approach that resolves this problem by estimating context-dependent change in dynamic parameters in single-subject time series models. The approach examines parameter changes of known shape and thus addresses the problem of observed intra-individual heterogeneity (e.g., changes in emotional dynamics due to observed changes in daily stress). In comparison to existing approaches to unobserved heterogeneity, model estimation is facilitated and different forms of change can readily be accommodated. We demonstrate the approach's viability given relatively short time series by means of a simulation study. In addition, we present an empirical application, targeting the joint dynamics of affect and stress and how these co-vary with daily events. We discuss potentials and limitations of the approach and close with an outlook on the broader implications for understanding emotional adaption and development.     

Normal Versus Noncentral Chi-square Asymptotics of Misspecified Models

In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences of ignoring spatial dependence. Specifically, we find inefficiency in the estimates of the factor score means and bias and inefficiency in the estimates of the corresponding covariance matrix. We apply the model to Schwartz value priority data obtained from 5 European countries. We show that the Schwartz motivational types of values, such as Conformity, Tradition, Benevolence, and Hedonism, possess high spatial autocorrelation. We identify several spatial patterns—specifically, Conformity and Hedonism have a country-specific structure, Tradition has a North–South gradient that cuts across national borders, and Benevolence has South–North cross-national gradient. Finally, we show that conventional factor analysis may lead to a loss of valuable insights compared with the proposed approach.     

Multilevel Dynamic Generalized Structured Component Analysis for Brain Connectivity Analysis in Functional Neuroimaging Data

We extend dynamic generalized structured component analysis (GSCA) to enhance its data-analytic capability in structural equation modeling of multi-subject time series data. Time series data of multiple subjects are typically hierarchically structured, where time points are nested within subjects who are in turn nested within a group. The proposed approach, named multilevel dynamic GSCA, accommodates the nested structure in time series data. Explicitly taking the nested structure into account, the proposed method allows investigating subject-wise variability of the loadings and path coefficients by looking at the variance estimates of the corresponding random effects, as well as fixed loadings between observed and latent variables and fixed path coefficients between latent variables. We demonstrate the effectiveness of the proposed approach by applying the method to the multi-subject functional neuroimaging data for brain connectivity analysis, where time series data-level measurements are nested within subjects.     

An examination of the first/second-grade form of the pictorial scale of perceived competence and social acceptance: Factor structure and stability by grade and gender across groups of economically disadvantaged children

We tested the structure of the Pictorial Scale of Competence and Social Acceptance (PSPCSA) across groups of first and second grade children from economically disadvantaged backgrounds. We used confirmatory factor analysis, including latent mean structures analysis, to test the fit of competing PSPCSA factor models and examined invariance across time and gender. Cohort 1 data were used to find a best fitting model. Cohorts 2 and 3 data were used for model cross-validation and invariance testing across time. Gender differences were examined with the multiple indicators, multiple causes model. We found support for a time invariant three-factor model but uncovered issues of concern related to score reliability. Consistent with the hypothesized decline in children's early optimistic bias, we found a statistically significant moderate decline in perceptions of cognitive and peer competence over time. In addition, we identified differences between boys and girls: (a) on perceptions of cognitive competence and (b) across several items within each of the PSPCSA subscales.     

Fractal models for event-based and dynamical timers

Some recent papers proposed to distinguish between event-based and emergent timing. Event-based timing is conceived as prescribed by events produced by a central clock, and seems to be used in discrete tasks (e.g., finger tapping). Emergent or dynamical timing refers to the exploitation of the dynamical properties of effectors, and is typically used in continuous tasks (e.g., circle drawing). The analysis of period series suggested that both timing control processes possess fractal properties, characterized by self-similarity and long-range dependence. The aim of this article is to present two models that produce period series presenting the statistical properties previously evidenced in discrete and continuous rhythmic tasks. The first one is an adaptation of the classical activation/threshold models, including a plateau-like evolution of the threshold over time. The second one is a hybrid limit-cycle model, including a time-dependent linear stiffness parameter. Both models reproduced satisfactorily the spectral signatures of event-based and dynamical timing processes, respectively. The models also produced auto-correlation functions similar to those experimentally observed. Using ARFIMA modeling we show that these simulated series possess fractal properties. We suggest in conclusion some possible extensions of this modeling approach, to account for the effects of metronomic pacing, or to analyze bimanual coordination.     

TARGET ARTICLE: On Building a Better Process Model: It's Not Only How Many,but Which Ones and By Which Means?

The Quad Model proposes that four cognitive processes are pervasive across social behavior. I describe the model and compare it to dual- and uniprocess models. Distinguishing among the four processes can provide a more nuanced and accurate depiction of social behavior than can other models. It also allows the model to be applied to a much broader range of domains. A key problem for many dual-process models is that they confound processing style with either type of content (e.g., category vs. individuating information) or type of task (implicit vs. explicit tasks). As a result, these models have trouble assessing the joint influences of multiple processes. In contrast, the Quad Model provides estimates of the independent and simultaneous contributions of 4 key processes to social behavior.