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

Abstract

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.

Exploring network structure and central items of the Narcissistic Personality Inventory

“…An Ising Model (IM) was estimated from our dataset. An IM (Marsman et al, 2018;van Borkulo et al, 2014) is the binary equivalent of the Gaussian Graphical Model used for continuous datasets (Epskamp et al, 2017). A lasso (least absolute shrinkage and selection operator) was used to provide a conservative network structure (Epskamp & Fried, 2018).…”

Network Models for Cognitive Development and Intelligence

“…β is related to the general connectivity parameter in (3). That this Ising model is equivalent to a special case of the multivariate 2-parameter logistic IRT model is shown in several papers [57,[59][60]. Here the temperature relates to the item discrimination parameters in the 2-parameter logistic model.…”

“…Several papers describe the relationship between the Ising model and other statistical models, such as the loglinear model, logistic regression, collider models, and item response theory models [57][58][59][60], a relation that is based on the work of Kac [61]. In particular, these papers demonstrate the statistical equivalence between the Ising model and multidimensional item response theory (MIRT) models.…”

Use of the Ages and Stages Questionnaires to Establish Indicators of Child Development in Public Daycare Centers in Rio De Janeiro, Brazil

“…Multimethod assessments such as interviews, direct observation, and self-reporting, as well as quantitative tools such as tests and scales are accessible to psychologists (Hilsenroth, Segal, & Hersen, 2003). However, from this group of methods the use of tests, inventories, scales, and other quantitative tools are seen as the best choices when one needs to accurately measure psychological traits (Borsboom, Mellenbergh, & van Heerden, 2003;Craig, 2017;Marsman et al, 2018;Novick, 1980), as long as they are psychometrically adequate.…”

“…The second approach understands constructs as reflexive and the presence of the construct is assumed to be the common cause of the observed variables. The statistical model most often associated with this idea is the Principal Component Analysis (PCA) model, and the two major statistical models associated with the reflective model are the common factor model and the Item Response Theory (IRT) (Edwards & Bagozzi, 2000;Marsman et al, 2018). Image 1 below displays these conceptualizations.…”