A growing number of publications focus on estimating Gaussian graphical models (GGM, networks of partial correlation coefficients). At the same time, generalizibility and replicability of these highly parameterized models are debated, and sample sizes typically found in datasets may not be sufficient for estimating the underlying network structure. In addition, while recent work emerged that aims to compare networks based on different samples, these studies do not take potential cross-study heterogeneity into account. To this end, this paper introduces methods for estimating GGMs by aggregating over multiple datasets. We first introduce a general maximum likelihood estimation modeling framework in which all discussed models are embedded. This modeling framework is subsequently used to introduce meta-analytic Gaussian network aggregation (MAGNA). We discuss two variants: fixed-effects MAGNA, in which heterogeneity across studies is not taken into account, and random-effects MAGNA, which models sample correlations and takes heterogeneity into account. We assess the performance of MAGNA in large-scale simulation studies. Finally, we exemplify the method using four datasets of post-traumatic stress disorder (PTSD) symptoms, and summarize findings from a larger meta-analysis of PTSD symptom.

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.

Graphical models have received an increasing amount of attention in network psychometrics as a promising probabilistic approach to study the conditional relations among variables using graph theory. Despite recent advances, existing methods on graphical models usually assume a homogeneous population and focus on binary or continuous variables. However, ordinal variables are very popular in many areas of psychological science, and the population often consists of several different groups based on the heterogeneity in ordinal data. Driven by these needs, we introduce the finite mixture of ordinal graphical models to effectively study the heterogeneous conditional dependence relationships of ordinal data. We develop a penalized likelihood approach for model estimation, and design a generalized expectation-maximization (EM) algorithm to solve the significant computational challenges. We examine the performance of the proposed method and algorithm in simulation studies. Moreover, we demonstrate the potential usefulness of the proposed method in psychological science through a real application concerning the interests and attitudes related to fan avidity for students in a large public university in the United States.

Network analysis is an increasingly popular approach to study mental disorders in all their complexity. Multiple methods have been developed to extract networks from cross-sectional data, with these data being either continuous or binary. However, when it comes to time series data, most efforts have focused on continuous data. We therefore propose ConNEcT, a network approach for binary symptom data across time. ConNEcT allows to visualize and study the prevalence of different symptoms as well as their co-occurrence, measured by means of a contingency measure in one single network picture. ConNEcT can be complemented with a significance test that accounts for the serial dependence in the data. To illustrate the usefulness of ConNEcT, we re-analyze data from a study in which patients diagnosed with major depressive disorder weekly reported the absence or presence of eight depression symptoms. We first extract ConNEcTs for all patients that provided data during at least 104 weeks, revealing strong inter-individual differences in which symptom pairs co-occur significantly. Second, to gain insight into these differences, we apply Hierarchical Classes Analysis on the co-occurrence patterns of all patients, showing that they can be grouped into meaningful clusters. Core depression symptoms (i.e., depressed mood and/or diminished interest), cognitive problems and loss of energy seem to co-occur universally, but preoccupation with death, psychomotor problems or eating problems only co-occur with other symptoms for specific patient subgroups.

Common outputs of software programs for network estimation include association matrices containing the edge weights between pairs of symptoms and a plot of the symptom network. Although such outputs are useful, it is sometimes difficult to ascertain structural relationships among symptoms from these types of output alone. We propose that matrix permutation provides a simple, yet effective, approach for clarifying the order relationships among the symptoms based on the edge weights of the network. For directed symptom networks, we use a permutation criterion that has classic applications in electrical circuit theory and economics. This criterion can be used to place symptoms that strongly predict other symptoms at the beginning of the ordering, and symptoms that are strongly predicted by other symptoms at the end. For undirected symptom networks, we recommend a permutation criterion that is based on location theory in the field of operations research. When using this criterion, symptoms with many strong ties tend to be placed centrally in the ordering, whereas weakly-tied symptoms are placed at the ends. The permutation optimization problems are solved using dynamic programming. We also make use of branch-search algorithms for extracting maximum cardinality subsets of symptoms that have perfect structure with respect to a selected criterion. Software for implementing the dynamic programming algorithms is available in MATLAB and R. Two networks from the literature are used to demonstrate the matrix permutation algorithms.

The past few years were marked by increased online offensive strategies perpetrated by state and non-state actors to promote their political agenda, sow discord, and question the legitimacy of democratic institutions in the US and Western Europe. In 2016, the US congress identified a list of Russian state-sponsored Twitter accounts that were used to try to divide voters on a wide range of issues. Previous research used latent Dirichlet allocation (LDA) to estimate latent topics in data extracted from these accounts. However, LDA has characteristics that may limit the effectiveness of its use on data from social media: The number of latent topics must be specified by the user, interpretability of the topics can be difficult to achieve, and it does not model short-term temporal dynamics. In the current paper, we propose a new method to estimate latent topics in texts from social media termed Dynamic Exploratory Graph Analysis (DynEGA). In a Monte Carlo simulation, we compared the ability of DynEGA and LDA to estimate the number of simulated latent topics. The results show that DynEGA is substantially more accurate than several different LDA algorithms when estimating the number of simulated topics. In an applied example, we performed DynEGA on a large dataset with Twitter posts from state-sponsored right- and left-wing trolls during the 2016 US presidential election. DynEGA revealed topics that were pertinent to several consequential events in the election cycle, demonstrating the coordinated effort of trolls capitalizing on current events in the USA. This example demonstrates the potential power of our approach for revealing temporally relevant information from qualitative text data.

The combination of network theory and network psychometric methods has opened up a variety of new ways to conceptualize and study psychological disorders. The idea of psychological disorders as dynamic systems has sparked interest in developing interventions based on results of network analytic tools. However, simply estimating a network model is not sufficient for determining which symptoms might be most effective to intervene upon, nor is it sufficient for determining the potential efficacy of any given intervention. In this paper, we attempt to remedy this gap by introducing fundamental concepts of control theory to both psychometricians and applied psychologists. We introduce two controllability statistics to the psychometric literature, average and modal controllability, to facilitate selecting the best set of intervention targets. Following this introduction, we show how intervention scientists can probe the effects of both theoretical and empirical interventions on networks derived from real data and demonstrate how simulations can account for intervention cost and the desire to reduce specific symptoms. Every step is based on rich clinical EMA data from a sample of subjects undergoing treatment for complicated grief, with a focus on the outcome suicidal ideation. All methods are implemented in an open-source R package netcontrol, and complete code for replicating the analyses in this manuscript are available online.

Network analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

This commentary reflects on the articles included in the Psychometrika Special Issue on Network Psychometrics in Action. The contributions to the special issue are related to several possible future paths for research in this area. These include the development of models to analyze and represent interventions, improvement in exploratory and inferential techniques in network psychometrics, the articulation of psychometric theories in addition to psychometric models, and extensions of network modeling to novel data sources. Finally, network psychometrics is part of a larger movement in psychology that revolves around the analysis of human beings as complex systems, and it is timely that psychometricians start extending their rich modeling tradition to improve and extend the analysis of systems in psychology.

This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course. The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative “validation” of the factor model, using auxiliary information about the popularity of items consulted during an open-book examination in the course.

Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which—respect to the second-order confirmatory factor analysis—is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated with the related factor and, therefore, the associated factor loadings are constrained to be nonnegative. A cyclic block coordinate descent algorithm is proposed to maximize the likelihood. We present a simulation study that investigates the ability to get reliable factors. Furthermore, the new model is applied to identify the underlying factors of well-being showing the characteristics of the new methodology. A final discussion completes the paper.

Recently, machine learning (ML) methods have been used in causal inference to estimate treatment effects in order to reduce concerns for model mis-specification. However, many ML methods require that all confounders are measured to consistently estimate treatment effects. In this paper, we propose a family of ML methods that estimate treatment effects in the presence of cluster-level unmeasured confounders, a type of unmeasured confounders that are shared within each cluster and are common in multilevel observational studies. We show through simulation studies that our proposed methods are robust from biases from unmeasured cluster-level confounders in a variety of multilevel observational studies. We also examine the effect of taking an algebra course on math achievement scores from the Early Childhood Longitudinal Study, a multilevel observational educational study, using our methods. The proposed methods are available in the CURobustML R package.

Major depression is a severe mental disorder that is associated with strongly increased mortality. The quantification of its prevalence on regional levels represents an important indicator for public health reporting. In addition to that, it marks a crucial basis for further explorative studies regarding environmental determinants of the condition. However, assessing the distribution of major depression in the population is challenging. The topic is highly sensitive, and national statistical institutions rarely have administrative records on this matter. Published prevalence figures as well as available auxiliary data are typically derived from survey estimates. These are often subject to high uncertainty due to large sampling variances and do not allow for sound regional analysis. We propose a new area-level Poisson mixed model that accounts for measurement errors in auxiliary data to close this gap. We derive the empirical best predictor under the model and present a parametric bootstrap estimator for the mean squared error. A method of moments algorithm for consistent model parameter estimation is developed. Simulation experiments are conducted to show the effectiveness of the approach. The methodology is applied to estimate the major depression prevalence in Germany on regional levels crossed by sex and age groups.