Pairwise Markov Random Fields

Abstract

This chapter introduces pairwise Markov random fields (PMRFs), a class of models of which the parameters can be represented as an undirected network. In this undirected network nodes represent variables and edges represent the strength of association between two variables after conditioning on all other variables included in the model. The chapter focuses on specific classes of PMRFs often used in network psychometrics: Gaussian graphical models (GGM; a network of partial correlations) for continuous data, Ising models for binary data, and mixed graphical models (MGM) for data with different types of variables. PMRFs can be interpreted in multiple ways: the models can be used as a general statistical modeling framework, as an exploratory tool to investigate predictive relationships between variables, as a tool to generate causal hypotheses, as a causal model itself, and as an exploratory tool to uncover latent variables. The chapter concludes with an introduction to estimating PMRFs from data using the bootnet and psychonetrics packages.