Network Psychometrics in Educational Practice: Maximum Likelihood Estimation of the Curie-Weiss Model

Abstract

In network psychometrics undirected graphical models—such as the Ising model from statistical physics—are used to characterize the manifest probability distribution of psychometric data. In practice, we often find that it is extremely difficult to apply graphical models as the Ising model to educational data because (i) the model’s likelihood is impossible to compute for the big data that we typically observe in educational measurement, and (ii) the model cannot handle the partially observed data that stem from incomplete test designs. In this chapter, we therefore propose to use a simplified Ising model that is known as the Curie-Weiss model. Unlike the more general Ising model, the Curie-Weiss model is computationally tractable, which makes it suitable for applications in educational measurement. The objective of this chapter is to study the statistical properties of the Curie-Weiss model and discuss its estimation with complete or incomplete data. We demonstrate that our procedures work using a simulated example, and illustrate the analysis of fit of the Curie-Weiss model using real data from the 2012 Cito Eindtoets.