Symposium: The Emerging Field of Bayesian Graphical Modeling in Psychology

Network psychometrics uses undirected graphical models to model the network structure of complex psychosocial systems. This talk will introduce Bayesian graphical modeling, the Bayesian approach to the analysis of psychological networks and the topic of this symposium. Estimating the causal structure of a psychosocial system from correlational data is extremely difficult, so the field has focused instead on estimating the conditional independence and dependence structure. In this context, Markov Random Field (MRF) models are an important class of undirected graphical models because their parameters provide direct information about the conditional independence structure of the underlying system. We discuss new and old MRF models for psychological variables, especially binary and ordinal variables, and the computational and conceptual challenges in their Bayesian analysis. The ultimate goal of these analyses is the Bayes factor test of conditional independence, and we discuss how this significantly advances the field of network psychometrics.

This is an in-person presentation on July 20, 2023 (11:00 ~ 11:20 UTC).

Network models have become a popular tool for studying multivariate dependencies in psychological data. The most popular models are the Ising model for binary data and the Gaussian Graphical Model (GGM) for continuous data. However, most cross-sectional data are in fact ordinal. For example, personality questionnaires are scored on Likert scales, symptoms are rated in ordered categories of severity, and opinions and attitudes are measured on scales ranging from strong disagreement to strong agreement. Recently, however, appropriate network models for ordinal data have been developed that eliminate the need to binarize the data or model ordinal variables as continuous. In this paper, we discuss existing network models for ordinal data that either use a latent continuous distribution or model ordinal variables as manifest variables. We then provide a large-scale simulation study that evaluates the absolute and relative performance of these ordinal network models and contrasts them with the misspecified GGM. Based on these results, we discuss the advantages and disadvantages of each method and provide guidance as to when each method is most appropriate.

This is an in-person presentation on July 20, 2023 (11:20 ~ 11:40 UTC).

In recent years, graphical models have gained interest in psychology for modelling relationships between variables. On of the most popular models is the Ising model for binary data. The model contains parameters for the main effects of the variables as well as interaction parameters between the variables. Estimating these parameters is challenging due to the intractable normalising constant in the probability density function. For this reason, the straightforward method of maximum likelihood estimation can only be used for small networks (up to 15 nodes). For larger networks, approximate methods are used, in particular the joint pseudo-likelihood method is often used. This method is known to be consistent. However, for finite samples, not much is known about how well it estimates parameters. In addition to this method, other approximate likelihood methods are often used for parameter estimation, such as the independent conditional likelihood method, which evaluates the conditional likelihood of each variable given the rest of the variables separately, or methods that try to simplify the normalizing constant, which we call the observed population method. In this talk, an overview of all these parameter estimation methods is provided. First theoretically, discussing the advantages and shortcomings of each method. Secondly, a simulation study will provide insights into how the methods actually perform against each other under different circumstances, such as varying network structures and different graph and sample sizes.

This is an in-person presentation on July 20, 2023 (11:40 ~ 10:02 UTC).

The Gaussian graphical model (GGM) is often used to estimate the network structure of high-dimensional data. However, the standard Gaussian graphical model does not describe hierarchical structures in the data, which frequently occur in empirical research. For example, in fMRI studies, each participant has an individual network, but participants are also related as they form a population. Nevertheless, a common approach to analyze such data is to fit a GGM for each participant individually, thereby neglecting the shared variance. This talk discusses an extension of the GGM that describes hierarchical data. We relate the networks of individuals using Markov random field priors on the edge structure. Specifically, we use the Ising model and the Curie-Weiss model as Markov random field priors. This approach simultaneously captures the shared variance between the graph structure of different individuals and estimates a group-level network. The method is illustrated with an application on resting state fMRI data.

This is an in-person presentation on July 20, 2023 (12:00 ~ 12:20 UTC).

In network psychometrics, constructs are oftentimes argued to map onto causal structures. Researchers have developed the graphical approach to causal inference as a formal framework in which causal relationships are represented as directed acyclic graphs (DAGs). It is difficult to model the directed, causal structures from correlational data; conditional dependencies and independencies are key to identifying DAGs that are consistent with observed data. The Bayesian approach provides three main methods that can test for conditional independence within graphical models: the credible interval, the Bayes factor, and the Bayesian model-averaged inclusion Bayes factor. In this talk, we will provide an introduction to these three approaches, highlight their strengths and limitations, and discuss a small-scale simulation study comparing the performance of these methods. Using the Bayesian model-averaging approach, we introduce the edge evidence plot for network psychometrics. The edge evidence plot visualizes the conditional (in)dependence relationship between variables. Its use will be illustrated with an example in the field of psychopathology. As such, in this last talk of the symposium, we aim to highlight the benefits of adopting the Bayesian approach to network analysis for applied researchers.

This is an in-person presentation on July 20, 2023 (12:20 ~ 12:40 UTC).