Subgrouping with Chain Graphical VAR Models.

Recent years have seen the emergence of an "idio-thetic" class of methods to bridge the gap between nomothetic and idiographic inference. These methods describe nomothetic trends in idiographic processes by pooling intraindividual information across individuals to inform group-level inference or vice versa. The current work introduces a novel "idio-thetic" model: the subgrouped chain graphical vector autoregression (scGVAR). The scGVAR is unique in its ability to identify subgroups of individuals who share common dynamic network structures in both lag(1) and contemporaneous effects. Results from Monte Carlo simulations indicate that the scGVAR shows promise over similar approaches when clusters of individuals differ in their contemporaneous dynamics and in showing increased sensitivity in detecting nuanced group differences while keeping Type-I error rates low. In contrast, a competing approach-the Alternating Least Squares VAR (ALS VAR) performs well when groups were separated by larger distances. Further considerations are provided regarding applications of the ALS VAR and scGVAR on real data and the strengths and limitations of both methods.

Evaluating Discrete Time Methods for Subgrouping Continuous Processes.

Rapid developments over the last several decades have brought increased focus and attention to the role of time scales and heterogeneity in the modeling of human processes. To address these emerging questions, subgrouping methods developed in the discrete-time framework-such as the vector autoregression (VAR)-have undergone widespread development to identify shared nomothetic trends from idiographic modeling results. Given the dependence of VAR-based parameters on the measurement intervals of the data, we sought to clarify the strengths and limitations of these methods in recovering subgroup dynamics under different measurement intervals. Building on the work of Molenaar and collaborators for subgrouping individual time-series by means of the subgrouped chain graphical VAR (scgVAR) and the subgrouping option in the group iterative multiple model estimation (S-GIMME), we present results from a Monte Carlo study aimed at addressing the implications of identifying subgroups using these discrete-time methods when applied to continuous-time data. Results indicate that discrete-time subgrouping methods perform well at recovering true subgroups when the measurement intervals are large enough to capture the full range of a system's dynamics, either via lagged or contemporaneous effects. Further implications and limitations are discussed therein.

Describing and Controlling Multivariate Nonlinear Dynamics: A Boolean Network Approach.

We introduce a discrete-time dynamical system method, the Boolean network method, that may be useful for modeling, studying, and controlling nonlinear dynamics in multivariate systems, particularly when binary time-series are available. We introduce the method in three steps: inference of the temporal relations as Boolean functions, extraction of attractors and assignment of desirability based on domain knowledge, and design of network control to direct a psychological system toward a desired attractor. To demonstrate how the Boolean network can describe and prescribe control for emotion regulation dynamics, we applied this method to data from a study of how children use bidding to an adult and/or distraction to regulate their anger during a frustrating task (N = 120, T = 480 seconds). Network control strategies were designed to move the child into attractors where anger is OFF. The sample shows heterogeneous emotion regulation dynamics across children in 22 distinct Boolean networks, and heterogeneous control strategies regarding which behavior to perturb and how to perturb it. The Boolean network method provides a novel method to describe nonlinear dynamics in multivariate psychological systems and is a method with potential to eventually inform the design of interventions that can guide those systems toward desired goals.

A Square-Root Second-Order Extended Kalman Filtering Approach for Estimating Smoothly Time-Varying Parameters.

Researchers collecting intensive longitudinal data (ILD) are increasingly looking to model psychological processes, such as emotional dynamics, that organize and adapt across time in complex and meaningful ways. This is also the case for researchers looking to characterize the impact of an intervention on individual behavior. To be useful, statistical models must be capable of characterizing these processes as complex, time-dependent phenomenon, otherwise only a fraction of the system dynamics will be recovered. In this paper we introduce a Square-Root Second-Order Extended Kalman Filtering approach for estimating smoothly time-varying parameters. This approach is capable of handling dynamic factor models where the relations between variables underlying the processes of interest change in a manner that may be difficult to specify in advance. We examine the performance of our approach in a Monte Carlo simulation and show the proposed algorithm accurately recovers the unobserved states in the case of a bivariate dynamic factor model with time-varying dynamics and treatment effects. Furthermore, we illustrate the utility of our approach in characterizing the time-varying effect of a meditation intervention on day-to-day emotional experiences.

Problems with Centrality Measures in Psychopathology Symptom Networks: Why Network Psychometrics Cannot Escape Psychometric Theory.

Understanding patterns of symptom co-occurrence is one of the most difficult challenges in psychopathology research. Do symptoms co-occur because of a latent factor, or might they directly and causally influence one another? Motivated by such questions, there has been a surge of interest in network analyses that emphasize the putatively direct role symptoms play in influencing each other. In this critical paper, we highlight conceptual and statistical problems with using centrality measures in cross-sectional networks. In particular, common network analyses assume that there are no unmodeled latent variables that confound symptom co-occurrence. The traditions of clinical taxonomy and test development in psychometric theory, however, greatly increase the possibility that latent variables exist in symptom data. In simulations that include latent variables, we demonstrate that closeness and betweenness are vulnerable to spurious covariance among symptoms that connect subgraphs (e.g., diagnoses). We further show that strength is redundant with factor loading in several cases. Finally, if a symptom reflects multiple latent causes, centrality metrics reflect a weighted combination, undermining their interpretability in empirical data. Our results suggest that it is essential for network psychometric approaches to examine the evidence for latent variables prior to analyzing or interpreting patterns at the symptom level. Failing to do so risks identifying spurious relationships or failing to detect causally important effects. Altogether, we argue that centrality measures do not provide solid ground for understanding the structure of psychopathology when latent confounding exists.

A Tribute to the Mind, Methodology and Mentoring of Wayne Velicer.

Wayne Velicer is remembered for a mind where mathematical concepts and calculations intrigued him, behavioral science beckoned him, and people fascinated him. Born in Green Bay, Wisconsin on March 4, 1944, he was raised on a farm, although early influences extended far beyond that beginning. His Mathematics BS and Psychology minor at Wisconsin State University in Oshkosh, and his PhD in Quantitative Psychology from Purdue led him to a fruitful and far-reaching career. He was honored several times as a high-impact author, was a renowned scholar in quantitative and health psychology, and had more than 300 scholarly publications and 54,000+ citations of his work, advancing the arenas of quantitative methodology and behavioral health. In his methodological work, Velicer sought out ways to measure, synthesize, categorize, and assess people and constructs across behaviors and time, largely through principal components analysis, time series, and cluster analysis. Further, he and several colleagues developed a method called Testing Theory-based Quantitative Predictions, successfully applied to predicting outcomes and effect sizes in smoking cessation, diet behavior, and sun protection, with the potential for wider applications. With $60,000,000 in external funding, Velicer also helped engage a large cadre of students and other colleagues to study methodological models for a myriad of health behaviors in a widely applied Transtheoretical Model of Change. Unwittingly, he has engendered indelible memories and gratitude to all who crossed his path. Although Wayne Velicer left this world on October 15, 2017 after battling an aggressive cancer, he is still very present among us.

Affect and Personality: Ramifications of Modeling (Non-)Directionality in Dynamic Network Models.

The use of dynamic network models has grown in recent years. These models allow researchers to capture both lagged and contemporaneous effects in longitudinal data typically as variations, reformulations, or extensions of the standard vector autoregressive (VAR) models. To date, many of these dynamic networks have not been explicitly compared to one another. We compare three popular dynamic network approaches-GIMME, uSEM, and LASSO gVAR-in terms of their differences in modeling assumptions, estimation procedures, statistical properties based on a Monte Carlo simulation, and implications for affect and personality researchers. We found that all three approaches dynamic networks provided yielded group-level empirical results in partial support of affect and personality theories. However, individual-level results revealed a great deal of heterogeneity across approaches and participants. Reasons for discrepancies are discussed alongside these approaches' respective strengths and limitations.

Evaluating the organizational structure and specificity of network topology within the face processing system.

There is increasing appreciation that network-level interactions among regions produce components of face processing previously ascribed to individual regions. Our goals were to use an exhaustive data-driven approach to derive and quantify the topology of directed functional connections within a priori defined nodes of the face processing network and evaluate whether the topology is category-specific. Young adults were scanned with fMRI as they viewed movies of faces, objects, and scenes. We employed GIMME to model effective connectivity among core and extended face processing regions, which allowed us to evaluate all possible directional connections, under each viewing condition (face, object, place). During face processing, we observed directional connections from the right posterior superior temporal sulcus to both the right occipital face area and right fusiform face area (FFA), which does not reflect the topology reported in prior studies. We observed connectivity between core and extended regions during face processing, but this limited to a feed-forward connection from the FFA to the amygdala. Finally, the topology of connections was unique to face processing. These findings suggest that the pattern of directed functional connections within the face processing network, particularly in the right core regions, may not be as hierarchical and feed-forward as described previously. Our findings support the notion that topologies of network connections are specialized, emergent, and dynamically responsive to task demands.

Granger Causality Testing with Intensive Longitudinal Data.

The availability of intensive longitudinal data obtained by means of ambulatory assessment opens up new prospects for prevention research in that it allows the derivation of subject-specific dynamic networks of interacting variables by means of vector autoregressive (VAR) modeling. The dynamic networks thus obtained can be subjected to Granger causality testing in order to identify causal relations among the observed time-dependent variables. VARs have two equivalent representations: standard and structural. Results obtained with Granger causality testing depend upon which representation is chosen, yet no criteria exist on which this important choice can be based. A new equivalent representation is introduced called hybrid VARs with which the best representation can be chosen in a data-driven way. Partial directed coherence, a frequency-domain statistic for Granger causality testing, is shown to perform optimally when based on hybrid VARs. An application to real data is provided.

The Impact of Variation in Twin Relatedness on Estimates of Heritability and Environmental Influences.

By taking advantage of the natural variation in genetic relatedness among identical (monozygotic: MZ) and fraternal (dizygotic: DZ) twins, twin studies are able to estimate genetic and environmental contributions to complex human behaviors. Recently concerns have been raised about the accuracy of twin studies in light of findings of genetic and epigenetic changes in twins. One of the concerns raised is that MZ twins are not 100% genetically and epigenetically similar because they show variations in their genomes and epigenomes leading to inaccurate estimates of heritability. This article presents findings from a simulation study that examined the degree of bias in estimates of heritability and environmentality when the genetic and epigenetic similarity of MZ twins differs from 1.00 and when the genetic and epigenetic similarity of DZ twins differs from 0.50. The findings suggest that in the standard biometric model when MZ or DZ twin similarity differs from 1.00 or 0.50, respectively, the variance that should be attributed to genetic influences is instead attributed to nonshared environmental influences, thus deflating the estimates of genetic influences and inflating the estimates of nonshared environmental influences. Although estimates of genetic and nonshared environmental influences from the standard biometric model were found to deviate from "true" values, the bias was usually smaller than 10% points indicating that the interpretations of findings from previous twin studies are mostly correct.

Real-time visual feedback of COM and COP motion properties differentially modifies postural control structures.

The experiment was setup to investigate the control of human quiet standing through the manipulation of augmented visual information feedback of selective properties of the motion of two primary variables in postural control: center of pressure (COP) and center of mass (COM). Five properties of feedback information were contrasted to a no feedback dual-task (watching a movie) control condition to determine the impact of visual real-time feedback on the coordination of the joint motions in postural control in both static and dynamic one-leg standing postures. The feedback information included 2D COP or COM position and macro variables derived from the COP and COM motions, namely virtual time-to-contact (VTC) and the COP-COM coupling. The findings in the static condition showed that the VTC and COP-COM coupling feedback conditions decreased postural motion more than the 2D COP or COM positional information. These variables also induced larger sway amplitudes in the dynamic condition showing a more progressive search strategy in exploring the stability limits. Canonical correlation analysis (CCA) found that COP-COM coupling contributed less than the other feedback variables to the redundancy of the system reflected in the common variance between joint motions and properties of sway motion. The COP-COM coupling had the lowest weighting of the motion properties to redundancy under the feedback conditions but overall the qualitative pattern of the joint motion structures was preserved within the respective static and dynamic balance conditions.

Equivalent Dynamic Models.

Equivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.

(Re)evaluating the Implications of the Autoregressive Latent Trajectory Model Through Likelihood Ratio Tests of Its Initial Conditions.

The autoregressive latent trajectory (ALT) model synthesizes the autoregressive model and the latent growth curve model. The ALT model is flexible enough to produce a variety of discrepant model-implied change trajectories. While some researchers consider this a virtue, others have cautioned that this may confound interpretations of the model's parameters. In this article, we show that some-but not all-of these interpretational difficulties may be clarified mathematically and tested explicitly via likelihood ratio tests (LRTs) imposed on the initial conditions of the model. We show analytically the nested relations among three variants of the ALT model and the constraints needed to establish equivalences. A Monte Carlo simulation study indicated that LRTs, particularly when used in combination with information criterion measures, can allow researchers to test targeted hypotheses about the functional forms of the change process under study. We further demonstrate when and how such tests may justifiably be used to facilitate our understanding of the underlying process of change using a subsample (N = 3,995) of longitudinal family income data from the National Longitudinal Survey of Youth.

State space modeling of time-varying contemporaneous and lagged relations in connectivity maps.

Most connectivity mapping techniques for neuroimaging data assume stationarity (i.e., network parameters are constant across time), but this assumption does not always hold true. The authors provide a description of a new approach for simultaneously detecting time-varying (or dynamic) contemporaneous and lagged relations in brain connectivity maps. Specifically, they use a novel raw data likelihood estimation technique (involving a second-order extended Kalman filter/smoother embedded in a nonlinear optimizer) to determine the variances of the random walks associated with state space model parameters and their autoregressive components. The authors illustrate their approach with simulated and blood oxygen level-dependent functional magnetic resonance imaging data from 30 daily cigarette smokers performing a verbal working memory task, focusing on seven regions of interest (ROIs). Twelve participants had dynamic directed functional connectivity maps: Eleven had one or more time-varying contemporaneous ROI state loadings, and one had a time-varying autoregressive parameter. Compared to smokers without dynamic maps, smokers with dynamic maps performed the task with greater accuracy. Thus, accurate detection of dynamic brain processes is meaningfully related to behavior in a clinical sample.

Person-Specific Non-shared Environmental Influences in Intra-individual Variability: A Preliminary Case of Daily School Feelings in Monozygotic Twins.

Most behavioural genetic studies focus on genetic and environmental influences on inter-individual phenotypic differences at the population level. The growing collection of intensive longitudinal data in social and behavioural science offers a unique opportunity to examine genetic and environmental influences on intra-individual phenotypic variability at the individual level. The current study introduces a novel idiographic approach and one novel method to investigate genetic and environmental influences on intra-individual variability by a simple empirical demonstration. Person-specific non-shared environmental influences on intra-individual variability of daily school feelings were estimated using time series data from twenty-one pairs of monozygotic twins (age = 10 years, 16 female pairs) over two consecutive weeks. Results showed substantial inter-individual heterogeneity in person-specific non-shared environmental influences. The current study represents a first step in investigating environmental influences on intra-individual variability with an idiographic approach, and provides implications for future behavioural genetic studies to examine developmental processes from a microscopic angle.

Dealing with Multiple Solutions in Structural Vector Autoregressive Models.

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.

A Rejoinder.

Three commentaries on the Nesselroade and Molenaar target article in this issue are responded to in the interest of elaborating and defending the points of view expressed in our article. The commentaries feature philosophy of science, general structural modeling, and broad behavioral research perspectives. Responding to the commentaries afforded us the opportunity to clarify further matters that we deem critical to the fundamental matter of measurement in behavioral science, especially as it emphasizes (properly, we believe) the individual as the primary unit of analysis.

Some Behaviorial Science Measurement Concerns and Proposals.

Primarily from a measurement standpoint, we question some basic beliefs and procedures characterizing the scientific study of human behavior. The relations between observed and unobserved variables are key to an empirical approach to building explanatory theories and we are especially concerned about how the former are used as proxies for the latter. We believe that behavioral science can profitably reconsider the prevailing version of this arrangement because of its vulnerability to limiting idiosyncratic aspects of observed/unobserved variable relations. We describe a general measurement approach that takes into account idiosyncrasies that should be irrelevant to the measurement process but can intrude and may invalidate it in ways that distort and weaken relations among theoretically important variables. To clarify further our major concerns, we briefly describe one version of the measurement approach that fundamentally supports the individual as the primary unit of analysis orientation that we believe should be preeminent in the scientific study of human behavior.

Networks involved in olfaction and their dynamics using independent component analysis and unified structural equation modeling.

The study of human olfaction is complicated by the myriad of processing demands in conscious perceptual and emotional experiences of odors. Combining functional magnetic resonance imaging with convergent multivariate network analyses, we examined the spatiotemporal behavior of olfactory-generated blood-oxygenated-level-dependent signal in healthy adults. The experimental functional magnetic resonance imaging (fMRI) paradigm was found to offset the limitations of olfactory habituation effects and permitted the identification of five functional networks. Analysis delineated separable neuronal circuits that were spatially centered in the primary olfactory cortex, striatum, dorsolateral prefrontal cortex, rostral prefrontal cortex/anterior cingulate, and parietal-occipital junction. We hypothesize that these functional networks subserve primary perceptual, affective/motivational, and higher order olfactory-related cognitive processes. Results provided direct evidence for the existence of parallel networks with top-down modulation for olfactory processing and clearly distinguished brain activations that were sniffing-related versus odor-related. A comprehensive neurocognitive model for olfaction is presented that may be applied to broader translational studies of olfactory function, aging, and neurological disease.