Get Over It! A Multilevel Threshold Autoregressive Model for State-Dependent Affect Regulation

Reciprocal effects between negative affect and emotion regulation in daily life

The extended process model of emotion regulation provides a framework for understanding how emotional experiences and emotion regulation (ER) mutually influence each other over time. To investigate this reciprocal relationship, 202 adults completed a ten-day experience-sampling survey capturing levels of negative affect (NA) experience and use of ten ER strategies in daily life. Residual dynamic structural equation models (DSEMs) were used to examine within-person cross-lagged and autoregressive effects of NA and ER (strategy use and between-strategy variability). Results showed that NA predicted lower between-strategy variability, lower subsequent use of acceptance and problem-solving, but higher subsequent use of rumination and worry. Moreover, reappraisal and between-strategy variability predicted lower subsequent NA levels, while expressive suppression and worry predicted higher subsequent NA levels. Stable autoregressive effects were found for NA and for maladaptive ER strategies (e.g., rumination and worry). Exploratory correlation analyses revealed positive associations between NA inertia and maladaptive ER strategies. Together, these findings provide evidence of a dynamic interplay between NA and ER. This work deepens how we understand the challenges of applying ER strategies in daily life. Future clinical and translational research should consider these dynamic perspectives on ER and affect.

Variation in emotion dynamics over time is associated with future relationship outcomes

Romantic relationships are defined by emotion dynamics, or how the emotions of one partner at a single timepoint can affect their own emotions and the emotions of their partner at the next timepoint. Previous research has shown that the level of these emotion dynamics plays a role in determining the state and quality of the relationship. However, this research has not examined whether the estimated emotion dynamics change over time, and how the change in these dynamics might relate to relationship outcomes, despite changes in dynamics being likely to occur. We examined whether the magnitude of variation in emotion dynamics over time was associated with relationship outcomes in a sample of 148 couples. Time-varying vector autoregressive models were used to estimate the emotion dynamics for each couple, and the average and standard deviation of the dynamics over time was related to relationship quality and relationship dissolution 1-2 years later. Our results demonstrate that certain autoregressive and cross-lagged parameters do show significant variation over time, and that this variation is associated with relationship outcomes. Overall, this study demonstrates the importance of accounting for change in emotion dynamics over time, and the relevance of this change to the prediction of future outcomes.

Fitting Bayesian Stochastic Differential Equation Models with Mixed Effects through a Filtering Approach

Recent advances in technology contribute to a fast-growing number of studies utilizing intensive longitudinal data, and call for more flexible methods to address the demands that come with them. One issue that arises from collecting longitudinal data from multiple units in time is nested data, where the variability observed in such data is a mixture of within-unit changes and between-unit differences. This article aims to provide a model-fitting approach that simultaneously models the within-unit changes with differential equation models and accounts for between-unit differences with mixed effects. This approach combines a variant of the Kalman filter, the continuous-discrete extended Kalman filter (CDEKF), and the Markov chain Monte Carlo method often employed in the Bayesian framework through the platform Stan. At the same time, it utilizes Stan's functionality of numerical solvers for the implementation of CDEKF. For an empirical illustration, we applied this method in the context of differential equation models to an empirical dataset to explore the physiological dynamics and co-regulation between couples.

Output order effects in autobiographical memory in old age: further evidence for an emotional organisation

It is generally accepted that autobiographical memories (AMs) are organised in associative networks. While both thematic and temporal similarity have been examined as connections among AMs, in the present study we focused on both the positive and negative emotional intensity of events as a possible link among AMs. To do so, we investigated whether the output order with which AMs elicited by cue words were reported can be accounted for emotional intensity of adjacent AMs. Data come from 94 older adults (M [Formula: see text] 67.14; SD [Formula: see text] 6.17) who reported 30 AMs in response to neutral cue words. Positive and negative emotional intensity of AMs were assessed on two separate scales (happiness and sadness). The output order was modeled based on a dual mixed-effects autoregressive model, where the strength of the autoregressive effect indicates how much the emotional intensity of an AM can be predicted by the emotional intensity of the previously reported AM. Results show that there were significant autoregressive effects for both the happiness and sadness ratings (accounting for 4% of variance). We also observed cross-over effects, such that the happiness rating of an AM was predicted by the sadness rating of the previously reported AM (and vice versa). Moreover, we found individual differences in the strength of the autoregressive effects. For the sadness ratings, these individual differences tended to be related to the participant's mood state, particularly so during the first output positions. Together, these findings demonstrate that there is a substantive effect of emotional intensity on the output order with which AMs are reported-even when elicited by cue words. Based on the premise that the output order of AMs informs about the organisation of autobiographical memory, our results highlight the role of emotional associations among AMs in old age.

Recovering Within-Person Dynamics from Psychological Time Series

Idiographic modeling is rapidly gaining popularity, promising to tap into the within-person dynamics underlying psychological phenomena. To gain theoretical understanding of these dynamics, we need to make inferences from time series models about the underlying system. Such inferences are subject to two challenges: first, time series models will arguably always be misspecified, meaning it is unclear how to make inferences to the underlying system; and second, the sampling frequency must be sufficient to capture the dynamics of interest. We discuss both problems with the following approach: we specify a toy model for emotion dynamics as the true system, generate time series data from it, and then try to recover that system with the most popular time series analysis tools. We show that making straightforward inferences from time series models about an underlying system is difficult. We also show that if the sampling frequency is insufficient, the dynamics of interest cannot be recovered. However, we also show that global characteristics of the system can be recovered reliably. We conclude by discussing the consequences of our findings for idiographic modeling and suggest a modeling methodology that goes beyond fitting time series models alone and puts formal theories at the center of theory development.

Dynamic structural equation modelling evaluating the progressively lowered stress threshold as an explanation for behavioural symptoms of dementia

Aim

To evaluate the progressively lowered stress threshold (PLST) conceptual model as an explanation for behavioural symptoms of dementia and test several of its hypothesized propositions. The PLST model suggests that due to impairments in coping, persons living with dementia have a reduced threshold for stress and respond with more behavioural symptoms of dementia as stress accumulates throughout the day.

Design

Intensive longitudinal design.

Methods

A sample of N = 165 family caregivers completed brief daily diary surveys for 21 days between the dates of 7/2019 and 8/2020, reporting on a total of 2841 days. Dynamic structural equation modelling was used as the analytic technique to examine the impact of caregiver and care recipient environmental stressors on the diversity of behavioural symptoms of dementia to account for the nested data structure and autoregressive relationships.

Findings

Results show direct relationships between environmental stressors and diversity of behavioural symptoms of dementia that same day and the following day.

Conclusion

Findings provide support for the PLST model propositions. Further, findings suggest an extension to the conceptual model is warranted given evidence of an exposure/recovery trajectory and the lagged effects of stress exposure on behavioural symptoms of dementia presentation.

Impact

This study tested whether a commonly used nursing model does in fact explain the occurrence of behavioural symptoms of dementia. The main findings support using the model as an intervention framework and suggest the model should be adapted to consider recovery trajectories. Since behavioural symptoms of dementia represent complex and dynamic temporal phenomena, traditional longitudinal assessments and analyses are an insufficient measurement modality for testing models. Findings inform the design of environmental‐modification type interventions for behavioural symptoms of dementia management and the methods to evaluate such interventions.

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.

Psychopathological networks: Theory, methods and practice

In recent years, network approaches to psychopathology have sparked much debate and have had a significant impact on how mental disorders are perceived in the field of clinical psychology. However, there are many important challenges in moving from theory to empirical research and clinical practice and vice versa. Therefore, in this article, we bring together different points of view on psychological networks by methodologists and clinicians to give a critical overview on these challenges, and to present an agenda for addressing these challenges. In contrast to previous reviews, we especially focus on methodological issues related to temporal networks. This includes topics such as selecting and assessing the quality of the nodes in the network, distinguishing between- and within-person effects in networks, relating items that are measured at different time scales, and dealing with changes in network structures. These issues are not only important for researchers using network models on empirical data, but also for clinicians, who are increasingly likely to encounter (person-specific) networks in the consulting room.

A Person- and Time-Varying Vector Autoregressive Model to Capture Interactive Infant-Mother Head Movement Dynamics

Head movement is an important but often overlooked component of emotion and social interaction. Examination of regularity and differences in head movements of infant-mother dyads over time and across dyads can shed light on whether and how mothers and infants alter their dynamics over the course of an interaction to adapt to each others. One way to study these emergent differences in dynamics is to allow parameters that govern the patterns of interactions to change over time, and according to person- and dyad-specific characteristics. Using two estimation approaches to implement variations of a vector-autoregressive model with time-varying coefficients, we investigated the dynamics of automatically-tracked head movements in mothers and infants during the Face-Face/Still-Face Procedure (SFP) with 24 infant-mother dyads. The first approach requires specification of a confirmatory model for the time-varying parameters as part of a state-space model, whereas the second approach handles the time-varying parameters in a semi-parametric ("mostly" model-free) fashion within a generalized additive modeling framework. Results suggested that infant-mother head movement dynamics varied in time both within and across episodes of the SFP, and varied based on infants' subsequently-assessed attachment security. Code for implementing the time-varying vector-autoregressive model using two R packages, dynr and mgcv, is provided.

A Markov Mixed-Effect Multinomial Logistic Regression Model for Nominal Repeated Measures with an Application to Syntactic Self-Priming Effects

Syntactic priming effects have been investigated for several decades in psycholinguistics and the cognitive sciences to understand the cognitive mechanisms that support language production and comprehension. The question of whether speakers prime themselves is central to adjudicating between two theories of syntactic priming, activation-based theories and expectation-based theories. However, there is a lack of a statistical model to investigate the two different theories when nominal repeated measures are obtained from multiple participants and items. This paper presents a Markov mixed-effect multinomial logistic regression model in which there are fixed and random effects for own-category lags and cross-category lags in a multivariate structure and there are category-specific crossed random effects (random person and item effects). The model is illustrated with experimental data that investigates the average and participant-specific deviations in syntactic self-priming effects. Results of the model suggest that evidence of self-priming is consistent with the predictions of activation-based theories. Accuracy of parameter estimates and precision is evaluated via a simulation study using Bayesian analysis.

Dynamics of sleep, sedentary behavior, and moderate-to-vigorous physical activity on school versus nonschool days

STUDY OBJECTIVES

Studies examining time-use activity behaviors (sleep, sedentary behavior, and physical activity) on school days compared with nonschool days have examined these behaviors independently, ignoring their interrelated nature, limiting our ability to optimize the health benefits of these behaviors. This study examines the associations of school-day (vs. nonschool day) with time-use activity behaviors.

METHODS

Time series data (6,642 days) from Fitbits (Charge-2) were collected (n = 196, 53% female, 5-10 years). We used a variable-centered dynamic structural equation modeling approach to estimate day-to-day associations of time-use activity behaviors on school days for each child. We then used person-centered cluster analyses to group individuals based on these estimates.

RESULTS

Within-participant analysis showed that on school days (vs. nonschool days), children (1) slept less (β = -0.17, 95% CI = -0.21, -0.13), (2) were less sedentary (β = -0.05, 95% CI = -0.09, -0.02), and (3) had comparable moderate-to-vigorous physical activity (MVPA; β = -0.05, 95% CI = -0.11, 0.00). Between-participant analysis showed that, on school days, children with higher sleep carryover experienced greater decreases in sleep (β = 0.44, 95% CI = 0.08, 0.71), children with higher body mass index z-score decreased sedentary behavior more (β = -0.41, 95% CI = -0.64, -0.13), and children with lower MVPA increased MVPA more (β = -0.41, 95% CI -0.64, -0.13). Cluster analysis demonstrated four distinct patterns of connections between time-use activity behaviors and school (High Activity, Sleep Resilient, High Sedentary, and Dysregulated Sleep).

CONCLUSIONS

Using a combination of person-centered and more traditional variable-centered approaches, we identified patterns of interrelated behaviors that differed on school, and nonschool days. Findings can inform targeted intervention strategies tailored to children's specific behavior patterns.

Order effects in the recall of autobiographical memories: evidence for an organisation along temporal and emotional features

Investigating the recall process of autobiographical memories (AMs) and, particularly, the order in which AMs are recalled has the potential to shed light on the organisation of autobiographical memory. However, research on order effects in the recall of AMs is relatively rare. Moreover, to date, no study addressed the question of where emotion fits into the organisation. The present study aimed to close this gap by examining whether emotional valence serves as one organising principle. Data come from 117 older adults (M = 74.11; SD = 7.06) who reported up to 39 AMs. The use of a multivariate multilevel model with autoregressive effects allows us to analyse the order effect within one person, as well as how the order effect differs between persons. The results replicated a temporal first-order effect that has been shown in previous studies and moreover, demonstrated a temporal second-order effect. Furthermore, our results indicated an emotional first-order effect that was even stronger than the temporal first-order effect and an emotional second-order effect. In addition, both first-order effects differed reliably between persons. Thus, the present study emphasises the need for considering emotion in current theoretical formulations of autobiographical memory and also of considering individual differences in the order of AMs recalled.

Exploring Idiographic Approaches to Children's Executive Function Performance: An Intensive Longitudinal Study

Traditional variable-centered research on executive functions (EFs) often infers intraindividual development using group-based averages. Such a method masks meaningful individuality and involves the fallacy of equating group-level data with person-specific changes. We used an intensive longitudinal design to study idiographic executive function fluctuation among ten boys from Grade 4. Each of the participants completed between 33 and 43 measurement occasions (M = 38.8) across approximately three months. Data were collected remotely using a computerized short version of the Dimensional Change Card Sort task. Multi-group analyses of three participant pairs (Participants 5 and 3, 5 and 2, and 5 and 6) demonstrated that Participant 5 differed from Participants 3 and 2 in different ways but Participants 5 and 6 were similar in all comparisons. Dynamic structural equation modeling demonstrated unique individual trajectories, which were not represented by the trajectory of group-averages. Although more than half of the participants showed a negative association between EFs and inattention, two participants showed a positive association between EF and inattention. This study demonstrated meaningful person-specific trajectories of EFs, suggesting that future study should undertake the analysis of individual development before data-aggregation or generalization from aggregate statistics to individuals.

Variability in emotion regulation strategy use is negatively associated with depressive symptoms

Variability in the emotion regulation (ER) strategies one uses throughout daily life has been suggested to reflect adaptive ER ability and to act as a protective factor in mental health. Moreover, psychological inflexibility and persistent negative affect (or affective inertia) are key features of depression and other forms of mental illness and are often further exacerbated by rigid or overly passive regulatory behaviours. The current study investigated the hypothesis that ER variability might serve as a protective factor against depressive symptoms and affective inertia. Using experience-sampling (N = 213), we tested whether two indictors of ER variability (between- and within-strategy SDs) were related to depressive symptoms and affective inertia. We found that people with higher between-strategy variability and within-strategy variability (specifically for reappraisal and distraction) reported fewer depressive symptoms. Both within- and between-strategy variability were negatively related to negative affective inertia. Between-strategy variability and negative affective inertia had unique effects on depression, when used as simultaneous predictors. Altogether, this study provides further evidence for the utility of ER as a factor buffering against depressive symptoms and particularly for the use of variable ER strategies.

Do Mothers or Children Lead the Dance? Disentangling Individual and Influence Effects During Conflict

Are mother-child conflict discussions shaped by time-varying, reciprocal influences, even after accounting for stable contributions from each individual? Mothers were filmed discussing a conflict for 5 min, separately with their younger (ages 5-9, N = 217) and older (ages 7-13, N = 220) children. Each person's conflict constructiveness was coded in 20-s intervals and data were analyzed using dynamic structural equation modeling, which separates individual and influence effects. Children influenced their mothers' behavior under certain conditions, with evidence for developmental differences in the magnitude and direction of influence, whereas mothers did not influence their children under any circumstance. Results are discussed in the context of child effects on parent behavior and changes in parenting across middle childhood.

Personality Pathology and Spouses' Moment-to-Moment Interpersonal Behaviors

We assessed the association of personality pathology with romantic couples' observed interpersonal behaviors. Couples engaged in four discussion tasks, after which observers used the Continuous Assessment of Interpersonal Dynamics method to continuously rate each participant's dominance and warmth over the course of each discussion. Using these ratings, we derived indices of average behaviors and changes in behaviors over the course of discussions. Generally, results indicated that the more personality pathology either spouse reported, the colder husbands were on average, and the colder they became toward their wives over time. However, personality disorder symptoms and overall interpersonal problems were largely unassociated with wives' behaviors. Results also indicated that the more dominance-related problems husbands and wives reported, the more dominantly and coldly they behaved, the more submissive or withdrawn their partners were, and the colder wives became over time; and the more warmth problems wives reported, the more dominantly, they behaved.

Affective Dynamics Across Internalizing and Externalizing Dimensions of Psychopathology

Little is known about pathogenic affective processes that cut across diverse mental disorders. The current study examines how dynamic features of positive and negative affect differ or converge across internalizing and externalizing disorders in a diagnostically diverse urban sample using bivariate dynamic structural equation modeling. One-hundred fifty-six young women completed semi-structured clinical interviews and a 21-day ecological momentary assessment protocol with seven assessments of affective states per day. Internalizing and externalizing dimensions of psychopathology were modeled using confirmatory factor analysis of mental disorders. After controlling for externalizing disorders, internalizing disorders were associated with higher negative affective mean intensity, higher negative affective variability (i.e., unique innovation variance), and lower positive affective variability. Conversely, externalizing disorders were associated with less persistent positive affect (i.e., lower inertia) and more variable positive emotionality. Results suggest internalizing and externalizing disorders have distinct affective dynamic signatures, which have implications for development of tailored interventions.

Featured Article: Bidirectional Effects of Sleep and Sedentary Behavior Among Toddlers: A Dynamic Multilevel Modeling Approach

OBJECTIVE

To examine the bidirectional effects of objectively measured nighttime sleep and sedentary activity among toddlers.

METHOD

Actical accelerometer data were analyzed for 195 toddlers participating in an obesity prevention trial (mean age = 27 months). Toddlers wore the accelerometers for up to 7 consecutive days. Nighttime sleep was defined as the number of minutes asleep between the hours of 8 pm and 8 am the following morning. Sedentary behavior (in minutes) was defined using previously established Actical cut points for toddlers. Variables were lagged and parsed into latent within- and between-person components, using dynamic structural equation modeling (DSEM).

RESULTS

Toddlers spent an average of 172 min (∼3 hr) in sedentary activity and slept an average of 460 min (∼8 hr) per night. An autoregressive cross-lagged multilevel model revealed significant autoregression for both sleep and sedentary activity. Cross-lagged values revealed that decreased sleep predicted increased next-day sedentary activity, and sedentary activity predicted that night's sleep. For 89% of the sample, the within-person standardized cross-lagged effects of sleep on sedentary were larger than the cross-lagged effects of sedentary on sleep.

CONCLUSIONS

Results suggest that, on average, nighttime sleep is a stronger predictor of subsequent sedentary behavior (compared with the reverse), and this is the case for the majority of toddlers. Findings highlight the importance of interindividual associations between sleep and sedentary activity. The present study is an example of how DSEM methods can be used to ask questions about Granger-causal cross-lagged relations between variables, both within and between individuals.

Using the time-varying autoregressive model to study dynamic changes in situation perceptions and emotional reactions

OBJECTIVE

Assuming personality to be a system of intra-individual processes emerging over time in interaction with the environment, we propose an idiographic approach to investigate potential changes of intra-individual dynamics in the perception of situations and emotions of individuals varying in personality traits. We compared the semiparametric time-varying autoregressive model (TV-AR) that takes into account the non-stationarity of psychological processes at the individual level, with the standard AR model.

METHOD

We conducted analyses of individual time series to assess intra-individual changes in mean levels and inertia on data from two adolescents who completed measures of personality and indicated their situation perceptions and emotions five times a day for 19 days.

RESULTS

For the less honest, emotional, extraverted, and more agreeable adolescent, the TV-AR model detected reliable changes in the intra-individual dynamics of situation perceptions and emotions whereas, for the other individual, the standard AR model was more preferred, given the lack of changes in the intra-individual dynamics.

CONCLUSIONS

Psychological processes dynamics in situation perception and emotions may vary from person to person depending on their personality. This work constitutes a first step in demonstrating that an idiographic approach has advantages in identifying changes in individuals' perceptions and reactions to situations.

Protective Buffering and Individual and Relational Adjustment Following Hematopoietic Stem Cell Transplantation: A Dyadic Daily-Diary Study

Background

Supportive communication (e.g., protective buffering, PB) may impact individual and relational adjustment in patients following hematopoietic stem cell transplantation (HSCT) and their caregivers. Previous studies revealed that PB (i.e., hiding one’s concerns and denying one’s worries) has mixed effects, namely it is beneficial, costly or unrelated to dyadic adjustment. This study aimed to verify these findings by addressing some unresolved issues, i.e., examining (1) both individual and relational as well as both positive and negative indicators of adjustment, (2) the effect of within-dyad congruence (i.e., complementarity/similarity) in PB, and (3) within-dyad causal associations between PB and adjustment.

Methods

Two hundred patients (following first autologous or allogeneic HSCT) and their caregivers independently completed measures of daily PB, relationship satisfaction, relationship stress, and positive affect (PA) and negative affect (NA) for 28 consecutive evenings after discharge of patients.

Findings

For both patients and caregivers, the results showed a same-day association between daily PB and individual (positive and negative) and relational (positive and negative) adjustment indicators showing the advantage of PB. In terms of the dyad congruence, complementarity (one partner high and the other low) in daily PB was related to higher same-day relationship satisfaction for both patients and caregivers and lower same-day relationship stress in caregivers. The benefits from similarity (both patient and caregiver high or low in PB) had delayed effects, although only in patients. As far as the causal associations were concerned, day-to-day changes in PB preceded changes in daily adjustment. In caregivers, reverse causality was found, i.e., changes in adjustment predicted next-day changes in support.

Discussion

Contrary to previous studies, daily PB has a rather beneficial effect in dyads following HSCT. Patients seemed to have benefited the most from the similarity in daily PB fluctuation, while caregivers profited from complementarity. Causal associations between PB and adjustment within-dyad were also different. The findings may add to a better understanding of PB-adjustment relationship in dyads facing HSCT.

At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the COGITO Study

With the growing popularity of intensive longitudinal research, the modeling techniques and software options for such data are also expanding rapidly. Here we use dynamic multilevel modeling, as it is incorporated in the new dynamic structural equation modeling (DSEM) toolbox in Mplus, to analyze the affective data from the COGITO study. These data consist of two samples of over 100 individuals each who were measured for about 100 days. We use composite scores of positive and negative affect and apply a multilevel vector autoregressive model to allow for individual differences in means, autoregressions, and cross-lagged effects. Then we extend the model to include random residual variances and covariance, and finally we investigate whether prior depression affects later depression scores through the random effects of the daily diary measures. We end with discussing several urgent-but mostly unresolved-issues in the area of dynamic multilevel modeling.

Modeling Nonstationary Emotion Dynamics in Dyads using a Time-Varying Vector-Autoregressive Model

Emotion dynamics are likely to arise in an interpersonal context. Standard methods to study emotions in interpersonal interaction are limited because stationarity is assumed. This means that the dynamics, for example, time-lagged relations, are invariant across time periods. However, this is generally an unrealistic assumption. Whether caused by an external (e.g., divorce) or an internal (e.g., rumination) event, emotion dynamics are prone to change. The semi-parametric time-varying vector-autoregressive (TV-VAR) model is based on well-studied generalized additive models, implemented in the software R. The TV-VAR can explicitly model changes in temporal dependency without pre-existing knowledge about the nature of change. A simulation study is presented, showing that the TV-VAR model is superior to the standard time-invariant VAR model when the dynamics change over time. The TV-VAR model is applied to empirical data on daily feelings of positive affect (PA) from a single couple. Our analyses indicate reliable changes in the male's emotion dynamics over time, but not in the female's-which were not predicted by her own affect or that of her partner. This application illustrates the usefulness of using a TV-VAR model to detect changes in the dynamics in a system.

Assessing Temporal Emotion Dynamics Using Networks

Multivariate psychological processes have recently been studied, visualized, and analyzed as networks. In this network approach, psychological constructs are represented as complex systems of interacting components. In addition to insightful visualization of dynamics, a network perspective leads to a new way of thinking about the nature of psychological phenomena by offering new tools for studying dynamical processes in psychology. In this article, we explain the rationale of the network approach, the associated methods and visualization, and illustrate it using an empirical example focusing on the relation between the daily fluctuations of emotions and neuroticism. The results suggest that individuals with high levels of neuroticism had a denser emotion network compared with their less neurotic peers. This effect is especially pronounced for the negative emotion network, which is in line with previous studies that found a denser network in depressed subjects than in healthy subjects. In sum, we show how the network approach may offer new tools for studying dynamical processes in psychology.

On the Use of Mixed Markov Models for Intensive Longitudinal Data

Markov modeling presents an attractive analytical framework for researchers who are interested in state-switching processes occurring within a person, dyad, family, group, or other system over time. Markov modeling is flexible and can be used with various types of data to study observed or latent state-switching processes, and can include subject-specific random effects to account for heterogeneity. We focus on the application of mixed Markov models to intensive longitudinal data sets in psychology, which are becoming ever more common and provide a rich description of each subject's process. We examine how specifications of a Markov model change when continuous random effect distributions are included, and how mixed Markov models can be used in the intensive longitudinal research context. Advantages of Bayesian estimation are discussed and the approach is illustrated by two empirical applications.

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.

A Comparison of Inverse-Wishart Prior Specifications for Covariance Matrices in Multilevel Autoregressive Models

Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices-the Inverse-Wishart distribution-tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.

Incorporating measurement error in n = 1 psychological autoregressive modeling

Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

A Multilevel AR(1) Model: Allowing for Inter-Individual Differences in Trait-Scores, Inertia, and Innovation Variance

In this article we consider a multilevel first-order autoregressive [AR(1)] model with random intercepts, random autoregression, and random innovation variance (i.e., the level 1 residual variance). Including random innovation variance is an important extension of the multilevel AR(1) model for two reasons. First, between-person differences in innovation variance are important from a substantive point of view, in that they capture differences in sensitivity and/or exposure to unmeasured internal and external factors that influence the process. Second, using simulation methods we show that modeling the innovation variance as fixed across individuals, when it should be modeled as a random effect, leads to biased parameter estimates. Additionally, we use simulation methods to compare maximum likelihood estimation to Bayesian estimation of the multilevel AR(1) model and investigate the trade-off between the number of individuals and the number of time points. We provide an empirical illustration by applying the extended multilevel AR(1) model to daily positive affect ratings from 89 married women over the course of 42 consecutive days.