Skewness and Staging: Does the Floor Effect Induce Bias in Multilevel AR(1) Models?

Multilevel autoregressive models are popular choices for the analysis of intensive longitudinal data in psychology. Empirical studies have found a positive correlation between autoregressive parameters of affective time series and the between-person measures of psychopathology, a phenomenon known as the staging effect. However, it has been argued that such findings may represent a statistical artifact: Although common models assume normal error distributions, empirical data (for instance, measurements of negative affect among healthy individuals) often exhibit the floor effect, that is response distributions with high skewness, low mean, and low variability. In this paper, we investigated whether-and to what extent-the floor effect leads to erroneous conclusions by means of a simulation study. We describe three dynamic models which have meaningful substantive interpretations and can produce floor-effect data. We simulate multilevel data from these models, varying skewness independent of individuals' autoregressive parameters, while also varying the number of time points and cases. Analyzing these data with the standard multilevel AR(1) model we found that positive bias only occurs when modeling with random residual variance, whereas modeling with fixed residual variance leads to negative bias. We discuss the implications of our study for data collection and modeling choices.

The within-between dispute in cross-lagged panel research and how to move forward.

How to model cross-lagged relations in panel data continues to be a source of disagreement in psychological research. While the cross-lagged panel model (CLPM) was the modeling approach of choice for many years, it has also been criticized repeatedly for its inability to separate within-person dynamics from stable between-person differences. Hence, various alternative models that disentangle these forms of variability have been proposed, and these are now rapidly gaining popularity. But not everyone agrees this is the right way forward. CLPM advocates point out that many psychological theories are concerned with longer-lasting differences between individuals, while these differences are not allowed to contribute to the estimation of cross-lagged effects in the novel within-between approaches. Reasoning this way, it is argued that the CLPM is superior when studying such processes, precisely because it includes the chronic between-person differences when estimating prospective effects. The goal of the current paper is to consider this within-between dispute in its broader context and to examine various directions in which this discussion needs expansion. To this end, three different perspectives are adopted: that of the study design, patterns in empirical data, and the nature of our research questions. It will be argued that to move forward, we need to look beyond the narrow focus on how to model our correlational panel data. Progress will involve theorizing more deliberately about the timescale that a process operates on, being more explicit about our research questions, considering alternative designs and models, and familiarizing ourselves with relevant discussions in other disciplines. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A tool to simulate and visualize dyadic interaction dynamics.

ynamic models are becoming increasingly popular to study the dynamic processes of dyadic interactions. In this article, we present a Dyadic Interaction Dynamics (DID) Shiny app which provides simulations and visualizations of data from several models that have been proposed for the analysis of dyadic data. We propose data generation as a tool to inspire and guide theory development and elaborate on how to connect substantive ideas to specific features of these models. We begin by discussing the basics of dynamic models with dyadic interactions. Then we present several models and illustrate model-implied behavior through generated data, accompanied by the DID Shiny app which allows researchers to generate and visualize their own data. Specifically, we consider: (a) the first-order vector autoregressive (VAR(1)) model; (b) the latent VAR(1) model; (c) the time-varying VAR(1) model; (d) the threshold VAR(1) model; (e) the hidden Markov model; and (f) the Markov-switching VAR(1) model. Finally, we demonstrate these models using empirical examples. We aim to give researchers more insight into what dynamic modeling approach fits their research question and data best. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality.

Network analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

From Data to Causes III: Bayesian Priors for General Cross-Lagged Panel Models (GCLM).

This article describes some potential uses of Bayesian estimation for time-series and panel data models by incorporating information from prior probabilities (i.e., priors) in addition to observed data. Drawing on econometrics and other literatures we illustrate the use of informative "shrinkage" or "small variance" priors (including so-called "Minnesota priors") while extending prior work on the general cross-lagged panel model (GCLM). Using a panel dataset of national income and subjective well-being (SWB) we describe three key benefits of these priors. First, they shrink parameter estimates toward zero or toward each other for time-varying parameters, which lends additional support for an income → SWB effect that is not supported with maximum likelihood (ML). This is useful because, second, these priors increase model parsimony and the stability of estimates (keeping them within more reasonable bounds) and thus improve out-of-sample predictions and interpretability, which means estimated effect should also be more trustworthy than under ML. Third, these priors allow estimating otherwise under-identified models under ML, allowing higher-order lagged effects and time-varying parameters that are otherwise impossible to estimate using observed data alone. In conclusion we note some of the responsibilities that come with the use of priors which, departing from typical commentaries on their scientific applications, we describe as involving reflection on how best to apply modeling tools to address matters of worldly concern.

Description, prediction and causation: Methodological challenges of studying child and adolescent development.

Scientific research can be categorized into: a) descriptive research, with the main goal to summarize characteristics of a group (or person); b) predictive research, with the main goal to forecast future outcomes that can be used for screening, selection, or monitoring; and c) explanatory research, with the main goal to understand the underlying causal mechanism, which can then be used to develop interventions. Since each goal requires different research methods in terms of design, operationalization, model building and evaluation, it should form an important basis for decisions on how to set up and execute a study. To determine the extent to which developmental research is motivated by each goal and how this aligns with the research designs that are used, we evaluated 100 publications from the Consortium on Individual Development (CID). This analysis shows that the match between research goal and research design is not always optimal. We discuss alternative techniques, which are not yet part of the developmental scientist's standard toolbox, but that may help bridge some of the lurking gaps that developmental scientists encounter between their research design and their research goal. These include unsupervised and supervised machine learning, directed acyclical graphs, Mendelian randomization, and target trials.

Time to get personal? The impact of researchers choices on the selection of treatment targets using the experience sampling methodology.

OBJECTIVE: One of the promises of the experience sampling methodology (ESM) is that a statistical analysis of an individual's emotions, cognitions and behaviors in everyday-life could be used to identify relevant treatment targets. A requisite for clinical implementation is that outcomes of such person-specific time-series analyses are not wholly contingent on the researcher performing them. METHODS: To evaluate this, we crowdsourced the analysis of one individual patient's ESM data to 12 prominent research teams, asking them what symptom(s) they would advise the treating clinician to target in subsequent treatment. RESULTS: Variation was evident at different stages of the analysis, from preprocessing steps (e.g., variable selection, clustering, handling of missing data) to the type of statistics and rationale for selecting targets. Most teams did include a type of vector autoregressive model, examining relations between symptoms over time. Although most teams were confident their selected targets would provide useful information to the clinician, not one recommendation was similar: both the number (0-16) and nature of selected targets varied widely. CONCLUSION: This study makes transparent that the selection of treatment targets based on personalized models using ESM data is currently highly conditional on subjective analytical choices and highlights key conceptual and methodological issues that need to be addressed in moving towards clinical implementation.

The fixed versus random effects debate and how it relates to centering in multilevel modeling.

In many disciplines researchers use longitudinal panel data to investigate the potentially causal relationship between 2 variables. However, the conventions and concerns vary widely across disciplines. Here we focus on 2 concerns, that is: (a) the concern about random effects versus fixed effects, which is central in the (micro)econometrics/sociology literature; and (b) the concern about grand mean versus group (or person) mean centering, which is central in the multilevel literature associated with disciplines like psychology and educational sciences. We show that these 2 concerns are actually addressing the same underlying issue. We discuss diverse modeling methods based on either multilevel regression modeling with the data in long format, or structural equation modeling with the data in wide format, and compare these approaches with simulated data. We extend the multilevel model with random slopes and discuss the consequences of this. Subsequently, we provide guidelines on how to choose between the diverse modeling options. We illustrate the use of these guidelines with an empirical example based on intensive longitudinal data, in which we consider both a time-varying and a time-invariant covariate. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

A primer on two-level dynamic structural equation models for intensive longitudinal data in Mplus.

Technological advances have led to an increase in intensive longitudinal data and the statistical literature on modeling such data is rapidly expanding, as are software capabilities. Common methods in this area are related to time-series analysis, a framework that historically has received little exposure in psychology. There is a scarcity of psychology-based resources introducing the basic ideas of time-series analysis, especially for data sets featuring multiple people. We begin with basics of N = 1 time-series analysis and build up to complex dynamic structural equation models available in the newest release of Mplus Version 8. The goal is to provide readers with a basic conceptual understanding of common models, template code, and result interpretation. We provide short descriptions of some advanced issues, but our main priority is to supply readers with a solid knowledge base so that the more advanced literature on the topic is more readily digestible to a larger group of researchers. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

A unified framework of longitudinal models to examine reciprocal relations.

Inferring reciprocal effects or causality between variables is a central aim of behavioral and psychological research. To address reciprocal effects, a variety of longitudinal models that include cross-lagged relations have been proposed in different contexts and disciplines. However, the relations between these cross-lagged models have not been systematically discussed in the literature. This lack of insight makes it difficult for researchers to select an appropriate model when analyzing longitudinal data, and some researchers do not even think about alternative cross-lagged models. The present research provides a unified framework that clarifies the conceptual and mathematical similarities and differences between these models. The unified framework shows that existing longitudinal models can be effectively classified based on whether the model posits unique factors and/or dynamic residuals and what types of common factors are used to model changes. The latter is essential to understand how cross-lagged parameters are interpreted. We also present an example using empirical data to demonstrate that there is great risk of drawing different conclusions depending on the cross-lagged models used. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Measurement error and person-specific reliability in multilevel autoregressive modeling.

An increasing number of researchers in psychology are collecting intensive longitudinal data in order to study psychological processes on an intraindividual level. An increasingly popular way to analyze these data is autoregressive time series modeling; either by modeling the repeated measures for a single individual using classic n = 1 autoregressive models, or by using multilevel extensions of these models, with the dynamics for each individual modeled at Level 1 and interindividual differences in these dynamics modeled at Level 2. However, while it is widely accepted in psychology that psychological measurements usually contain a certain amount of measurement error, the issue of measurement error is largely neglected in applied psychological (autoregressive) time series modeling: The regular autoregressive model incorporates innovations, or "dynamic errors," but not measurement error. In this article we discuss the concepts of reliability and measurement error in the context of dynamic (VAR(1)) models, and the consequences of disregarding measurement error variance in the data. For this purpose, we present a preliminary model that accounts for measurement error for constructs that are measured with a single indicator. We further discuss how this model could be used to investigate the between-person reliability of the measurements, as well as the (person-specific) within-person reliabilities and any individual differences in these reliabilities. We illustrate the consequences of assuming perfect reliability, the preliminary model, and reliabilities, using an empirical application in which we relate women's general positive affect to their positive affect concerning their romantic relationship. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

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.

Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data.

The Experience Sampling Method is a common approach in psychological research for collecting intensive longitudinal data with high ecological validity. One characteristic of ESM data is that it is often unequally spaced, because the measurement intervals within a day are deliberately varied, and measurement continues over several days. This poses a problem for discrete-time (DT) modeling approaches, which are based on the assumption that all measurements are equally spaced. Nevertheless, DT approaches such as (vector) autoregressive modeling are often used to analyze ESM data, for instance in the context of affective dynamics research. There are equivalent continuous-time (CT) models, but they are more difficult to implement. In this paper we take a pragmatic approach and evaluate the practical relevance of the violated model assumption in DT AR(1) and VAR(1) models, for the N = 1 case. We use simulated data under an ESM measurement design to investigate the bias in the parameters of interest under four different model implementations, ranging from the true CT model that accounts for all the exact measurement times, to the crudest possible DT model implementation, where even the nighttime is treated as a regular interval. An analysis of empirical affect data illustrates how the differences between DT and CT modeling can play out in practice. We find that the size and the direction of the bias in DT (V)AR models for unequally spaced ESM data depend quite strongly on the true parameter in addition to data characteristics. Our recommendation is to use CT modeling whenever possible, especially now that new software implementations have become available.

Paint it Black: Using Change-Point Analysis to Investigate Increasing Vulnerability to Depression towards the End of Vincent van Gogh's Life.

This study investigated whether Vincent van Gogh became increasingly self-focused-and thus vulnerable to depression-towards the end of his life, through a quantitative analysis of his written pronoun use over time. A change-point analysis was conducted on the time series formed by the pronoun use in Van Gogh's letters. We used time as a predictor to see whether there was evidence for increased self-focus towards the end of Van Gogh's life, and we compared this to the pattern in the letters written before his move to Arles. Specifically, we examined Van Gogh's use of first person singular pronouns (FPSP) and first person plural pronouns (FPPP) in the 415 letters he wrote while working as an artist before his move to Arles, and in the next 248 letters he wrote after his move to Arles until his death in Auvers-sur-Oise. During the latter period, Van Gogh's use of FPSP showed an annual increase of 0.68% (SE = 0.15, p < 0.001) and his use of FPPP showed an annual decrease of 0.23% (SE = 0.04, p < 0.001), indicating increasing self-focus and vulnerability to depression. This trend differed from Van Gogh's pronoun use in the former period (which showed no significant trend in FPSP, and an annual increase of FPPP of 0.03%, SE = 0.02, p = 0.04). This study suggests that Van Gogh's death was preceded by a gradually increasing self-focus and vulnerability to depression. It also illustrates how existing methods (i.e., quantitative linguistic analysis and change-point analysis) can be combined to study specific research questions in innovative ways.

Changing dynamics: Time-varying autoregressive models using generalized additive modeling.

In psychology, the use of intensive longitudinal data has steeply increased during the past decade. As a result, studying temporal dependencies in such data with autoregressive modeling is becoming common practice. However, standard autoregressive models are often suboptimal as they assume that parameters are time-invariant. This is problematic if changing dynamics (e.g., changes in the temporal dependency of a process) govern the time series. Often a change in the process, such as emotional well-being during therapy, is the very reason why it is interesting and important to study psychological dynamics. As a result, there is a need for an easily applicable method for studying such nonstationary processes that result from changing dynamics. In this article we present such a tool: the semiparametric TV-AR model. We show with a simulation study and an empirical application that the TV-AR model can approximate nonstationary processes well if there are at least 100 time points available and no unknown abrupt changes in the data. Notably, no prior knowledge of the processes that drive change in the dynamic structure is necessary. We conclude that the TV-AR model has significant potential for studying changing dynamics in psychology. (PsycINFO Database Record

What's in a Day? A Guide to Decomposing the Variance in Intensive Longitudinal Data.

In recent years there has been a growing interest in the use of intensive longitudinal research designs to study within-person processes. Examples are studies that use experience sampling data and autoregressive modeling to investigate emotion dynamics and between-person differences therein. Such designs often involve multiple measurements per day and multiple days per person, and it is not clear how this nesting of the data should be accounted for: That is, should such data be considered as two-level data (which is common practice at this point), with occasions nested in persons, or as three-level data with beeps nested in days which are nested in persons. We show that a significance test of the day-level variance in an empty three-level model is not reliable when there is autocorrelation. Furthermore, we show that misspecifying the number of levels can lead to spurious or misleading findings, such as inflated variance or autoregression estimates. Throughout the paper we present instructions and R code for the implementation of the proposed models, which includes a novel three-level AR(1) model that estimates moment-to-moment inertia and day-to-day inertia. Based on our simulations we recommend model selection using autoregressive multilevel models in combination with the AIC. We illustrate this method using empirical emotion data from two independent samples, and discuss the implications and the relevance of the existence of a day level for the field.

How to compare cross-lagged associations in a multilevel autoregressive model.

By modeling variables over time it is possible to investigate the Granger-causal cross-lagged associations between variables. By comparing the standardized cross-lagged coefficients, the relative strength of these associations can be evaluated in order to determine important driving forces in the dynamic system. The aim of this study was twofold: first, to illustrate the added value of a multilevel multivariate autoregressive modeling approach for investigating these associations over more traditional techniques; and second, to discuss how the coefficients of the multilevel autoregressive model should be standardized for comparing the strength of the cross-lagged associations. The hierarchical structure of multilevel multivariate autoregressive models complicates standardization, because subject-based statistics or group-based statistics can be used to standardize the coefficients, and each method may result in different conclusions. We argue that in order to make a meaningful comparison of the strength of the cross-lagged associations, the coefficients should be standardized within persons. We further illustrate the bivariate multilevel autoregressive model and the standardization of the coefficients, and we show that disregarding individual differences in dynamics can prove misleading, by means of an empirical example on experienced competence and exhaustion in persons diagnosed with burnout. (PsycINFO Database Record

Modeling BAS Dysregulation in Bipolar Disorder.

Time series analysis is a technique that can be used to analyze the data from a single subject and has great potential to investigate clinically relevant processes like affect regulation. This article uses time series models to investigate the assumed dysregulation of affect that is associated with bipolar disorder. By formulating a number of alternative models that capture different kinds of theoretically predicted dysregulation, and by comparing these in both bipolar patients and controls, we aim to illustrate the heuristic potential this method of analysis has for clinical psychology. We argue that, not only can time series analysis elucidate specific maladaptive dynamics associated with psychopathology, it may also be clinically applied in symptom monitoring and the evaluation of therapeutic interventions.

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

Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of this model is that the autoregressive parameter is treated as a fixed, trait-like property of a person. We argue that the autoregressive parameter may be state-dependent, for example, if the strength of affect regulation depends on the intensity of affect experienced. To allow such intra-individual variation, we propose a multilevel threshold autoregressive model. Using simulations, we show that this model can be used to detect state-dependent regulation with adequate power and Type I error. The potential of the new modeling approach is illustrated with two empirical applications that extend the basic model to address additional substantive research questions.