Recent Integrations of Latent Variable Network Modeling With Psychometric Models

The combination of network modeling and psychometric models has opened up exciting directions of research. However, there has been confusion surrounding differences among network models, graphic models, latent variable models and their applications in psychology. In this paper, I attempt to remedy this gap by briefly introducing latent variable network models and their recent integrations with psychometric models to psychometricians and applied psychologists. Following this introduction, I summarize developments under network psychometrics and show how graphical models under this framework can be distinguished from other network models. Every model is introduced using unified notations, and all methods are accompanied by available R packages inducive to further independent learning.

Discrete Latent Variable Models

We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. Algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation–maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.