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The majority of commentators agree on one thing: Our network approach might be the prime candidate for offering a new perspective on the origins of mental disorders. In our response, we elaborate on refinements (e.g., cognitive and genetic levels) and extensions (e.g., to Axis II disorders) of the network model, as well as discuss ways to test its validity. doi: 10.1017/S0140525X10000920

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy. Keywords: comorbidity; complex networks; generalized anxiety; latent variable models; major depression doi: 10.1017/S0140525X09991567

Several methods [model selection procedures (MSPs)] to determine the number of sources in electroencephalogram (EEG) and magnetoencphalogram (MEG) data have previously been investigated in an instantaneous analysis. In this paper, these MSPs are extended to a spatio-temporal analysis if possible. It is seen that the residual variance (RV) tends to overestimate the number of sources. The Akaike information criterion (AIC) and the Wald test on amplitudes (WA) and the Wald test on locations (WL) have the highest probabilities of selecting the correct number of sources. The WA has the advantage that it offers the opportunity to test which source is active at which time sample. Index Terms--Akaike criterion, Bayesian criterion, EEG, MEG, model order selection, source localization, testing source activity.

Interactions between cortical areas are crucial for cognitive functioning. Methods currently in use to assess such interactions are not well suited for this task because they lack timing precision, localization precision, or both. We present a method for simultaneous estimation of source location and orientation parameters and cross-spectral parameters to overcome these problems. Different estimators are evaluated for their performance. From a simulation study, we conclude that the estimators derived from the maximum-likelihood procedure have good statistical properties with moderate sample sizes, whereas those obtained from the generalized least squares procedure are biased and give poor-quality standard errors. The method is illustrated with visually evoked field data, with inconclusive results Index Terms--Coherence, covariance structures, cross-spectrum structures, EEG, frequency domain, functional connectivity, MEG, source modeling.

In electromagnetic source analysis, it is necessary to determine how many sources are required to describe the electroencephalogram or magnetoencephalogram adequately. Model selection procedures (MSPs) or goodness of fit procedures give an estimate of the required number of sources. Existing and new MSPs are evaluated in different source and noise settings: two sources which are close or distant and noise which is uncorrelated or correlated. The commonly used MSP residual variance is seen to be ineffective, that is it often selects too many sources. Alternatives like the adjusted Hotelling's test, Bayes information criterion and the Wald test on source amplitudes are seen to be effective. The adjusted Hotelling's test is recommended if a conservative approach is taken and MSPs such as Bayes information criterion or the Wald test on source amplitudes are recommended if a more liberal approach is desirable. The MSPs are applied to empirical data (visual evoked fields). Index Terms--EEG and MEG source analysis, goodness-of-fit, model selection, source localization, visual evoked fields.

The stationary dipole model for the inverse problem of magnetoencepholoographic (MEG) and electrencepholographic (EEG) data is extended. Spatio-temporal covariances of background noise are included.

A method is described to incorporate the spatiotemporal noise covariance matrix into a spatiotemporal source analysis. The essential feature is that the estimation problem is split into two parts. First, a model is fitted to the observed noise covariance matrix. This model is a Kronecker product of a spatial and a temporal matrix. The spatial matrix models the spatial covariances by a function dependent on sensor distance. The temporal matrix models the temporal covariances as lag dependent. In the second part, sources are estimated given this noise model, which can be done very efficiently due to the Kronecker formulation. An application to real electroencephalogram (EEG) data shows that the noise model fits the data very well. Simulation results show that the resulting source estimates are more precise than those obtained from a standard analysis neglecting the noise covariance. In addition, the estimated standard errors of the source parameter estimates are far more precise than those obtained from a standard analysis. Finally, the source parameter standard errors are used to investigate the effects of temporal sampling. It is shown that increasing the sampling by a factor x, decreases the standard errors of all source parameters with the square root of x. Index Terms--EEG/MEG source analysis, Kronecker product, parametric estimated generalized least squares, spatiotemporal noise covariance, temporal sampling.

The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alignment between positive (1) and negative (−1) atom spins. In many psychological applications, however, the Ising model is defined on the domain {0, 1} instead of the classical domain { − 1 , 1 }. While it is possible to transform the parameters of the Ising model in one domain to obtain a statistically equivalent model in the other domain, the parameters in the two versions of the Ising model lend themselves to different interpretations and imply different dynamics, when studying the Ising model as a dynamical system. In this tutorial paper, we provide an accessible discussion of the interpretation of threshold and interaction parameters in the two domains and show how the dynamics of the Ising model depends on the choice of domain. Finally, we provide a transformation that allows one to transform the parameters in an Ising model in one domain into a statistically equivalent Ising model in the other domain. [ABSTRACT FROM AUTHOR]

Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise interaction is independent of the values of all other variables. However, in psychological research, this is often implausible. In this article, we extend the GGM by allowing each pairwise interaction between two variables to be moderated by (a subset of) all other variables in the model, and thereby introduce a Moderated Network Model (MNM). We show how to construct MNMs and propose an ℓ 1 -regularized nodewise regression approach to estimate them. We provide performance results in a simulation study and show that MNMs outperform the split-sample based methods Network Comparison Test (NCT) and Fused Graphical Lasso (FGL) in detecting moderation effects. Finally, we provide a fully reproducible tutorial on how to estimate MNMs with the R-package mgm and discuss possible issues with model misspecification. [ABSTRACT FROM AUTHOR]

Networks are gaining popularity as an alternative to latent variable models for representing psychological constructs. Whereas latent variable approaches introduce unobserved common causes to explain the relations among observed variables, network approaches posit direct causal relations between observed variables. While these approaches lead to radically different understandings of the psychological constructs of interest, recent articles have established mathematical equivalences that hold between network models and latent variable models. We argue that the fact that for any model from one class there is an equivalent model from the other class does not mean that both models are equally plausible accounts of the data-generating mechanism. In many cases the constraints that are meaningful in one framework translate to constraints in the equivalent model that lack a clear interpretation in the other framework. Finally, we discuss three diverging predictions for the relation between zero-order correlations and partial correlations implied by sparse network models and unidimensional factor models. We propose a test procedure that compares the likelihoods of these models in light of these diverging implications. We use an empirical example to illustrate our argument. [ABSTRACT FROM AUTHOR]

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 by 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. [ABSTRACT FROM AUTHOR]

Summary: A new method is proposed to estimate graphical models simultaneously from data obtained at different coarseness scales. Starting from a predefined scale the method offers the possibility to zoom in or out over scales on particular edges. The estimated graphs over the different scales have similar structures although their level of sparsity depends on the scale at which estimation takes place. The method makes it possible to evaluate the evolution of the graphs from the coarsest to the finest scale or vice versa. We select an optimal coarseness scale to be used for further analysis. Simulation studies and an application on functional magnetic resonance brain imaging data show the method's performance in practice. [ABSTRACT FROM AUTHOR]

Estimated generalized least squares (EGLS) electromagnetic source analysis is used to downweight noisy and correlated data. Standard EGLS requires many trials to accurately estimate the noise covariances and, thus, the source parameters. Alternatively, the noise covariances can be modeled parametrically. Only the parameters of the model describing the noise covariances need to be estimated and, therefore, less trials are required. This method is referred to as parametric egls (PEGLS). In this paper, PEGLS is developed and its performance is tested in a simulation study and in a pseudoempirical study. Index Terms--EEG/MEG noise covariance, electromagnetic source analysis, estimated generalized least squares.