Objective Bayesian Edge Screening and Structure Selection for Ising Networks.

The Ising model is one of the most widely analyzed graphical models in network psychometrics. However, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our methods build on a continuous spike-and-slab approach. We show that our methods consistently select the correct structure and provide a new objective method to set the spike-and-slab hyperparameters. To circumvent the exploration of the complete structure space, which is too large in practical situations, we propose a novel approach that first screens for promising edges and then only explore the space instantiated by these edges. We apply our proposed methods to estimate the network of depression and alcohol use disorder symptoms from symptom scores of over 26,000 subjects.

A Note on the Structural Change Test in Highly Parameterized Psychometric Models.

Equal parameter estimates across subgroups is a substantial requirement of statistical tests. Ignoring subgroup differences poses a threat to study replicability, model specification, and theory development. Structural change tests are a powerful statistical technique to assess parameter invariance. A core element of those tests is the empirical fluctuation process. In the case of parameter invariance, the fluctuation process asymptotically follows a Brownian bridge. This asymptotic assumption further provides the basis for inference. However, the empirical fluctuation process does not follow a Brownian bridge in small samples, and this situation is amplified in large psychometric models. Therefore, common methods of obtaining the sampling distribution are invalid and the structural change test becomes conservative. We discuss an alternative solution to obtaining the sampling distribution-permutation approaches. Permutation approaches estimate the sampling distribution through resampling of the dataset, avoiding distributional assumptions. Hereby, the tests power are improved. We conclude that the permutation alternative is superior to standard asymptotic approximations of the sampling distribution.

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models.

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models-the Ising model from physics-and one of the most important latent variable models-the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.

Estimated generalized least squares electromagnetic source analysis based on a parametric noise covariance model.

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.

Connectionist investigations of individual differences in Stroop performance.

A simple connectionist model for the Stroop task was implemented to investigate a defective inhibition hypothesis first postulated by Fox in 1994 for individuals of high anxiety. Simulations with this model indicated that Stroop interference was positively, instead of negatively, related to inhibition. An alternative excitation hypothesis assuming that high anxiety corresponds to stronger verbal connections to the distracting material could also be investigated in the model. Stronger verbal connections indeed corresponded to larger interference. It is argued that this type of simulation could be useful, not because it proves in any way the supposed mechanisms, but because it clarifies the relation between theory and empirical data and so stimulates further specification of theoretical assumptions and invites empirical research into these assumptions.