In psychology, modeling multivariate dynamical processes within a person is gaining ground. A popular model is the lag-one vector autoregressive or VAR(1) model and its variants, in which each variable is regressed on all variables (including itself) at the previous time point. Many parameters have to be estimated in the VAR(1) model, however. The question thus rises whether the VAR(1) model is not too complex and overfits the data. If the latter is the case, the estimated model will not properly predict new unseen data. As a consequence, it cannot be trusted that the estimated parameters adequately characterize the individual from which the data at hand were sampled. In this article, we evaluate for current psychological applications whether the VAR(1) model outpredicts simpler models, using cross-validation (CV) techniques to determine the predictive accuracy. As it is unclear whether one should use standard CV techniques (leave-one-out CV or K-fold CV) or variants that take time dependence into account (blocked CV, hv-block CV, or accumulated prediction errors), we first compare the relative performance of these five CV techniques in a simulation study. The simulation settings mimic the data characteristics of current psychological VAR(1) applications and show that blocked CV has the best performance in general. Subsequently, we use blocked CV to assess to what extent the VAR(1) models predict unseen data for three recent psychological applications. We show that the VAR(1) based models do not outperform the AR(1) based ones for the three presented psychological applications. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

In psychology, studying multivariate dynamical processes within a person is gaining ground. An increasingly often used method is vector autoregressive (VAR) modeling, in which each variable is regressed on all variables (including itself) at the previous time points. This approach reveals the temporal dynamics of a system of related variables across time. A follow-up question is how to analyze data of multiple persons in order to grasp similarities and individual differences in within-person dynamics. We focus on the case where these differences are qualitative in nature, implying that subgroups of persons can be identified. We present a method that clusters persons according to their VAR regression weights, and simultaneously fits a shared VAR model to all persons within a cluster. The performance of the algorithm is evaluated in a simulation study. Moreover, the method is illustrated by applying it to multivariate time series data on depression-related symptoms of young women.

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.

The occurrence of concordance among different response components during an emotional episode is a key feature of several contemporary accounts and definitions of emotion. Yet, capturing such response concordance in empirical data has proven to be elusive, in large part because of a lack of appropriate statistical tools that are tailored to measure the intricacies of response concordance in the context of data on emotional responding. In this article, we present a tool we developed to detect two different forms of response concordance—response patterning and synchronization—in multivariate time series data of emotional responding, and apply this tool to data concerning physiological responding to emotional stimuli. While the findings provide partial evidence for both response patterning and synchronization, they also show that the presence and nature of such patterning and synchronization is strongly person-dependent.

Mixture analysis is commonly used for clustering objects on the basis of multivariate data. When the data contain a large number of variables, regular mixture analysis may become problematic, because a large number of parameters need to be estimated for each cluster. To tackle this problem, the mixtures-of-factor-analyzers (MFA) model was proposed, which combines clustering with exploratory factor analysis. MFA model selection is rather intricate, as both the number of clusters and the number of underlying factors have to be determined. To this end, the Akaike (AIC) and Bayesian (BIC) information criteria are often used. AIC and BIC try to identify a model that optimally balances model fit and model complexity. In this article, the CHull (Ceulemans & Kiers, 2006) method, which also balances model fit and complexity, is presented as an interesting alternative model selection strategy for MFA. In an extensive simulation study, the performances of AIC, BIC, and CHull were compared. AIC performs poorly and systematically selects overly complex models, whereas BIC performs slightly better than CHull when considering the best model only. However, when taking model selection uncertainty into account by looking at the first three models retained, CHull outperforms BIC. This especially holds in more complex, and thus more realistic, situations (e.g., more clusters, factors, noise in the data, and overlap among clusters).Keywords Mixture analysis . Model selection . AIC . BIC . CHullIn the behavioral sciences, researchers often cluster multivariate (i.e., object-by-variable) data in order to capture the heterogeneity that is present in the population. The resulting clusters can differ with regard to their level and/ or covariance structure. A first example pertains to the case in which a number of children are scored on certain psychopathological symptoms. The aim then is to discern different groups and to describe the differences between the groups in terms of the strength of the symptoms and/ or of their linear covariation. A second example is a consumer psychologist who wants to identify different groups of consumers on the basis of their appraisals of a wide range of food products.A commonly used clustering method is mixture analysis (McLachlan & Peel, 2000). In this method, each cluster is described by a different multivariate distribution, and every object belongs to each cluster with a particular probability. As a result, the full data follow a mixture of multivariate distributions. In practice, because of their computational simplicity, multivariate normal distributions are often assumed (McLachlan, Peel, & Bean, 2003), implying that each cluster is characterized by a mean vector and a covariance matrix.When the number of variables increases, such a mixture of multivariate normals may become problematic, in that a large number of variance and covariance parameters need to be estimated for each cluster [i.e., for J variables, J(J + 1)/2 variances and covariances need to be determined]. This problem is aggr...