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Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in many areas of psychological research time-varying parameters are plausible or even the subject of study. In this tutorial paper, we introduce methods to estimate time-varying VAR models based on splines and kernel-smoothing with/without regularization. We use simulations to evaluate the relative performance of all methods in scenarios typical in applied research, and discuss their strengths and weaknesses. Finally, we provide a step-by-step tutorial showing how to apply the discussed methods to an openly available time series of mood-related measurements.

Network models are an increasingly popular way to abstract complex psychological phenomena. While the study of the structure of network models has led to many important insights, little attention is paid to how well they predict observations. This is despite the fact that predictability is crucial for judging the practical relevance of edges: for instance in clinical practice, predictability of a symptom indicates whether a an intervention on that symptom through the symptom network is promising. We close this methodological gap by introducing nodewise predictability, which quantifies how well a given node can be predicted by all other nodes it is connected to in the network. In addition, we provide fully reproducible code examples of how to compute and visualize nodewise predictability both for cross-sectional and time-series data.

It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for different graph sizes (number of nodes) that the mean field approximation is accurate. The mean field approach allows us to provide possible explanations of 'jumping' behaviour in depression.

Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for sudden changes (phase transitions). Here, we show how a mean field approximation is used to reduce a dynamic multidimensional system to one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the risk that someone has for experiencing a transition. After validating the proposed method with simulated data, we apply this method to three empirical examples, where we validate our method using data that contains a transition, and where we show its use in a clinical and general sample. Results show an increased risk for a transition when the transition actually occurred, and that members of both the clinical and general sample were not susceptible to transitions from a healthy to a depressed mood, or vice versa. We conclude that the mean field approximation is valid to assess the risk for a transition, and could in the future aid clinical therapists in the treatment of depressed patient., Comment: The paper is changed and has a different title, thus we submitted the new version as a new preprint

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in 3 kinds of psychological datasets: datasets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered datasets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means---the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials., Comment: Accepted pending revision in Multivariate Behavioral Research

We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.

Undirected graphical models are a key component in the analysis of complex observational data in a large variety of disciplines. In many of these applications one is interested in estimating the undirected graphical model underlying a distribution over variables with different domains. Despite the pervasive need for such an estimation method, to date there is no such method that models all variables on their proper domain. We close this methodological gap by combining a new class of mixed graphical models with a structure estimation approach based on generalized covariance matrices. We report the performance of our methods using simulations, illustrate the method with a dataset on Autism Spectrum Disorder (ASD) and provide an implementation as an R-package.

Many psychologists do not realize that exploratory use of the popular multiway analysis of variance (ANOVA) harbors a multiple comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14% rather than 5% if the three tests are independent. We explain the multiple comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, the control of familywise error rate, the control of false discovery rate, and the preregistration of hypotheses.