Real-time detection of mean and variance changes in experience sampling data: A comparison of existing and novel statistical process control approaches.

Retrospective analyses of experience sampling (ESM) data have shown that changes in mean and variance levels may serve as early warning signs of an imminent depression. Detecting such early warning signs prospectively would pave the way for timely intervention and prevention. The exponentially weighted moving average (EWMA) procedure seems a promising method to scan ESM data for the presence of mean changes in real-time. Based on simulation and empirical studies, computing and monitoring day averages using EWMA works particularly well. We therefore expand this idea to the detection of variance changes and propose to use EWMA to prospectively scan for mean changes in day variability statistics (i.e., s 2 , s , ln( s )). When both mean and variance changes are of interest, the multivariate extension of EWMA (MEWMA) can be applied to both the day averages and a day statistic of variability. We evaluate these novel approaches to detecting variance changes by comparing them to EWMA-type procedures that have been specifically developed to detect a combination of mean and variance changes in the raw data: EWMA- S 2 , EWMA-ln( S 2 ), and EWMA- X ¯ - S 2 . We ran a simulation study to examine the performance of the two approaches in detecting mean, variance, or both types of changes. The results indicate that monitoring day statistics using (M)EWMA works well and outperforms EWMA- S 2 and EWMA-ln( S 2 ); the performance difference with EWMA- X ¯ - S 2 is smaller but notable. Based on the results, we provide recommendations on which statistic of variability to monitor based on the type of change (i.e., variance increase or decrease) one expects.

Chasing consistency: On the measurement error in self-reported affect in experiments.

How feelings change over time is a central topic in emotion research. To study these affective fluctuations, researchers often ask participants to repeatedly indicate how they feel on a self-report rating scale. Despite widespread recognition that this kind of data is subject to measurement error, the extent of this error remains an open question. Complementing many daily-life studies, this study aimed to investigate this question in an experimental setting. In such a setting, multiple trials follow each other at a fast pace, forcing experimenters to use a limited number of questions to measure affect during each trial. A total of 1398 participants completed a probabilistic reward task in which they were unknowingly presented with the same string of outcomes multiple times throughout the study. This allowed us to assess the test-retest consistency of their affective responses to the rating scales under investigation. We then compared these consistencies across different types of rating scales in hopes of finding out whether a given type of scale led to a greater consistency of affective measurements. Overall, we found moderate to good consistency of the affective measurements. Surprisingly, however, we found no differences in consistency across rating scales, which suggests that the specific rating scale that is used does not influence the measurement consistency.

Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU.

Computational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

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

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

The Affective Ising Model: A computational account of human affect dynamics.

The human affect system is responsible for producing the positive and negative feelings that color and guide our lives. At the same time, when disrupted, its workings lie at the basis of the occurrence of mood disorder. Understanding the functioning and dynamics of the affect system is therefore crucial to understand the feelings that people experience on a daily basis, their dynamics across time, and how they can become dysregulated in mood disorder. In this paper, a nonlinear stochastic model for the dynamics of positive and negative affect is proposed called the Affective Ising Model (AIM). It incorporates principles of statistical mechanics, is inspired by neurophysiological and behavioral evidence about auto-excitation and mutual inhibition of the positive and negative affect dimensions, and is intended to better explain empirical phenomena such as skewness, multimodality, and non-linear relations of positive and negative affect. The AIM is applied to two large experience sampling studies on the occurrence of positive and negative affect in daily life in both normality and mood disorder. It is examined to what extent the model is able to reproduce the aforementioned non-Gaussian features observed in the data, using two sightly different continuous-time vector autoregressive (VAR) models as benchmarks. The predictive performance of the models is also compared by means of leave-one-out cross-validation. The results indicate that the AIM is better at reproducing non-Gaussian features while their performance is comparable for strictly Gaussian features. The predictive performance of the AIM is also shown to be better for the majority of the affect time series. The potential and limitations of the AIM as a computational model approximating the workings of the human affect system are discussed.

Testing a computational model of subjective well-being: a preregistered replication of Rutledge et al. (2014).

Subjective well-being changes over time. While the causes of these changes have been investigated extensively, few attempts have been made to capture these changes through computational modelling. One notable exception is the study by Rutledge et al. [Rutledge, R. B., Skandali, N., Dayan, P., & Dolan, R. J. (2014). A computational and neural model of momentary subjective well-being. Proceedings of the National Academy of Sciences, 111(33), 12252-12257. https://doi.org/10.1073/pnas.1407535111], in which a model that captures momentary changes in subjective well-being was proposed. The model incorporates how an individual processes rewards and punishments in a decision context. Using this model, the authors were able to successfully explain fluctuations in subjective well-being observed in a gambling paradigm. Although Rutledge et al. reported an in-paper replication, a successful independent replication would further increase the credibility of their results. In this paper, we report a preregistered close replication of the behavioural experiment and analyses by Rutledge et al. The results of Rutledge et al. were mostly confirmed, providing further evidence for the role of rewards and punishments in subjective well-being fluctuations. Additionally, the association between personality traits and the way people process rewards and punishments was examined. No evidence for such associations was found, leaving this an open question for future research.

Prepaid parameter estimation without likelihoods.

In various fields, statistical models of interest are analytically intractable and inference is usually performed using a simulation-based method. However elegant these methods are, they are often painstakingly slow and convergence is difficult to assess. As a result, statistical inference is greatly hampered by computational constraints. However, for a given statistical model, different users, even with different data, are likely to perform similar computations. Computations done by one user are potentially useful for other users with different data sets. We propose a pooling of resources across researchers to capitalize on this. More specifically, we preemptively chart out the entire space of possible model outcomes in a prepaid database. Using advanced interpolation techniques, any individual estimation problem can now be solved on the spot. The prepaid method can easily accommodate different priors as well as constraints on the parameters. We created prepaid databases for three challenging models and demonstrate how they can be distributed through an online parameter estimation service. Our method outperforms state-of-the-art estimation techniques in both speed (with a 23,000 to 100,000-fold speed up) and accuracy, and is able to handle previously quasi inestimable models.

DstarM: an R package for analyzing two-choice reaction time data with the D∗M method.

The decision process in choice reaction time data is traditionally described in detail with diffusion models. However, the total reaction time is assumed to consist of the sum of a decision time (as modeled by the diffusion process) and the time devoted to nondecision processes (e.g., perceptual and motor processes). It has become standard practice to assume that the nondecision time is uniformly distributed. However, a misspecification of the nondecision time distribution introduces bias in the parameter estimates for the decision model. Recently, a new method has been proposed (called the D∗M method) that allows the estimation of the decision model parameters, while leaving the nondecision time distribution unspecified. In a second step, a nonparametric estimate of the nondecision time distribution may be retrieved. In this paper, we present an R package that estimates parameters of several diffusion models via the D∗M method. Moreover, it is shown in a series of extensive simulation studies that the parameters of the decision model and the nondecision distributions are correctly retrieved.

Detecting which variables alter component interpretation across multiple groups: A resampling-based method.

In psychology, many studies measure the same variables in different groups. In the case of a large number of variables when a strong a priori idea about the underlying latent construct is lacking, researchers often start by reducing the variables to a few principal components in an exploratory way. Herewith, one often wants to evaluate whether the components represent the same construct in the different groups. To this end, it makes sense to remove outlying variables that have significantly different loadings on the extracted components across the groups, hampering equivalent interpretations of the components. Moreover, identifying such outlying variables is important when testing theories about which variables behave similarly or differently across groups. In this article, we first scrutinize the lower bound congruence method (LBCM; De Roover, Timmerman, & Ceulemans in Behavior Research Methods, 49, 216-229, 2017), which was recently proposed for solving the outlying-variable detection problem. LBCM investigates how Tucker's congruence between the loadings of the obtained cluster-loading matrices improves when specific variables are discarded. We show that LBCM has the tendency to output outlying variables that either are false positives or concern very small, and thus practically insignificant, loading differences. To address this issue, we present a new heuristic: the lower and resampled upper bound congruence method (LRUBCM). This method uses a resampling technique to obtain a sampling distribution for the congruence coefficient, under the hypothesis that no outlying variable is present. In a simulation study, we show that LRUBCM outperforms LBCM. Finally, we illustrate the use of the method by means of empirical data.

Improved Insight into and Prediction of Network Dynamics by Combining VAR and Dimension Reduction.

To understand within-person psychological processes, one may fit VAR(1) models (or continuous-time variants thereof) to multivariate time series and display the VAR(1) coefficients as a network. This approach has two major problems. First, the contemporaneous correlations between the variables will frequently be substantial, yielding multicollinearity issues. In addition, the shared effects of the variables are not included in the network. Consequently, VAR(1) networks can be hard to interpret. Second, crossvalidation results show that the highly parametrized VAR(1) model is prone to overfitting. In this article, we compare the pros and cons of two potential solutions to both problems. The first is to impose a lasso penalty on the VAR(1) coefficients, setting some of them to zero. The second, which has not yet been pursued in psychological network analysis, uses principal component VAR(1) (termed PC-VAR(1)). In this approach, the variables are first reduced to a few principal components, which are rotated toward simple structure; then VAR(1) analysis (or a continuous-time analog) is applied to the rotated components. Reanalyzing the data of a single participant of the COGITO study, we show that PC-VAR(1) has the better predictive performance and that networks based on PC-VAR(1) clearly represent both the lagged and the contemporaneous variable relations.

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.

The Relation Between Valence and Arousal in Subjective Experience Varies With Personality and Culture.

OBJECTIVE: While in general arousal increases with positive or negative valence (a so-called V-shaped relation), there are large differences among individuals in how these two fundamental dimensions of affect are related in people's experience. In two studies, we examined two possible sources of this variation: personality and culture. METHOD: In Study 1, participants (Belgian university students) recalled a recent event that was characterized by high or low valence or arousal and reported on their feelings and their personality in terms of the Five-Factor Model. In Study 2, participants from Canada, China/Hong Kong, Japan, Korea, and Spain reported on their feelings in a thin slice of time and on their personality. RESULTS: In Study 1, we replicated the V-shape as characterizing the relation between valence and arousal, and identified personality correlates of experiencing particular valence-arousal combinations. In Study 2, we documented how the V-shaped relation varied as a function of Western versus Eastern cultural background and personality. CONCLUSIONS: The results showed that the steepness of the V-shaped relation between valence and arousal increases with Extraversion within cultures, and with a West-East distinction between cultures. Implications for the personality-emotion link and research on cultural differences in affect are discussed.

Critical slowing down as early warning for the onset and termination of depression.

About 17% of humanity goes through an episode of major depression at some point in their lifetime. Despite the enormous societal costs of this incapacitating disorder, it is largely unknown how the likelihood of falling into a depressive episode can be assessed. Here, we show for a large group of healthy individuals and patients that the probability of an upcoming shift between a depressed and a normal state is related to elevated temporal autocorrelation, variance, and correlation between emotions in fluctuations of autorecorded emotions. These are indicators of the general phenomenon of critical slowing down, which is expected to occur when a system approaches a tipping point. Our results support the hypothesis that mood may have alternative stable states separated by tipping points, and suggest an approach for assessing the likelihood of transitions into and out of depression.

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

Change point detection in multivariate time series is a complex task since next to the mean, the correlation structure of the monitored variables may also alter when change occurs. DeCon was recently developed to detect such changes in mean and\or correlation by combining a moving windows approach and robust PCA. However, in the literature, several other methods have been proposed that employ other non-parametric tools: E-divisive, Multirank, and KCP. Since these methods use different statistical approaches, two issues need to be tackled. First, applied researchers may find it hard to appraise the differences between the methods. Second, a direct comparison of the relative performance of all these methods for capturing change points signaling correlation changes is still lacking. Therefore, we present the basic principles behind DeCon, E-divisive, Multirank, and KCP and the corresponding algorithms, to make them more accessible to readers. We further compared their performance through extensive simulations using the settings of Bulteel et al. (Biological Psychology, 98 (1), 29-42, 2014) implying changes in mean and in correlation structure and those of Matteson and James (Journal of the American Statistical Association, 109 (505), 334-345, 2014) implying different numbers of (noise) variables. KCP emerged as the best method in almost all settings. However, in case of more than two noise variables, only DeCon performed adequately in detecting correlation changes.

Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model.

In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measures over time are modeled in terms of three person-specific parameters: a baseline level, intraindividual variation around the baseline, and regulatory mechanisms adjusting toward baseline. Variation due to measurement error is separated from meaningful intraindividual variation. The proposed model allows for the simultaneous analysis of longitudinal measurements of two linked variables (bivariate longitudinal modeling) and captures their relationship via two person-specific parameters. Relationships between explanatory variables and model parameters can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated simultaneously. Mathematical details of the approach, including a description of the core process model-the Ornstein-Uhlenbeck model-are provided. We also describe a user friendly, freely accessible software program that provides a straightforward graphical interface to carry out parameter estimation and inference. The proposed approach is illustrated by analyzing data collected via self-reports on affective states.

Using Raw VAR Regression Coefficients to Build Networks can be Misleading.

Many questions in the behavioral sciences focus on the causal interplay of a number of variables across time. To reveal the dynamic relations between the variables, their (auto- or cross-) regressive effects across time may be inspected by fitting a lag-one vector autoregressive, or VAR(1), model and visualizing the resulting regression coefficients as the edges of a weighted directed network. Usually, the raw VAR(1) regression coefficients are drawn, but we argue that this may yield misleading network figures and characteristics because of two problems. First, the raw regression coefficients are sensitive to scale and variance differences among the variables and therefore may lack comparability, which is needed if one wants to calculate, for example, centrality measures. Second, they only represent the unique direct effects of the variables, which may give a distorted picture when variables correlate strongly. To deal with these problems, we propose to use other VAR(1)-based measures as edges. Specifically, to solve the comparability issue, the standardized VAR(1) regression coefficients can be displayed. Furthermore, relative importance metrics can be computed to include direct as well as shared and indirect effects into the network.

Efficient simulation of diffusion-based choice RT models on CPU and GPU.

In this paper, we present software for the efficient simulation of a broad class of linear and nonlinear diffusion models for choice RT, using either CPU or graphical processing unit (GPU) technology. The software is readily accessible from the popular scripting languages MATLAB and R (both 64-bit). The speed obtained on a single high-end GPU is comparable to that of a small CPU cluster, bringing standard statistical inference of complex diffusion models to the desktop platform.

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times.

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.