mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data

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

Robust and Unbiased Variance of GLM Coefficients for Misspecified Autocorrelation and Hemodynamic Response Models in fMRI

As a consequence of misspecification of the hemodynamic response and noise variance models, tests on general linear model coe cients are not valid. Robust estimation of the variance of the general linear model (GLM) coecients in fMRI time series is therefore essential. In this paper an alternative method to estimate the variance of the GLM coe cients accurately is suggested and compared to other methods. The alternative, referred to as the sandwich, is based primarily on the fact that the time series are obtained from multiple exchangeable stimulus presentations. The analytic results show that the sandwich is unbiased. Using this result, it is possible to obtain an exact statistic which keeps the 5% false positive rate. Extensive Monte Carlo simulations show that the sandwich is robust against misspeci cation of the autocorrelations and of the hemodynamic response model. The sandwich is seen to be in many circumstances robust, computationally efficient, and flexible with respect to correlation structures across the brain. In contrast, the smoothing approach can be robust to a certain extent but only with specific knowledge of the circumstances for the smoothing parameter

A Tutorial on Estimating Time-Varying Vector Autoregressive Models

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

Computing assortative mixing by degree with the s-metric in networks using linear programming

Calculation of assortative mixing by degree in networks indicates whether nodes with similar degree are connected to each other. In networks with scale-free distribution high values of assortative mixing by degree can be an indication of a hub-like core in networks. Degree correlation has generally been used to measure assortative mixing of a network. But it has been shown that degree correlation cannot always distinguish properly between different networks with nodes that have the same degrees. The so-called -metric has been shown to be a better choice to calculate assortative mixing. The -metric is normalized with respect to the class of networks without self-loops, multiple edges, and multiple components, while degree correlation is always normalized with respect to unrestricted networks, where self-loops, multiple edges, and multiple components are allowed. The challenge in computing the normalized -metric is in obtaining the minimum and maximum value within a specific class of networks. We show that this can be solved by using linear programming. We use Lagrangian relaxation and the subgradient algorithm to obtain a solution to the -metric problem. Several examples are given to illustrate the principles and some simulations indicate that the solutions are generally accurate