Why does the Dyad-4PNO model of Kern and Culpepper (2020) fit real data?

This note aims to elucidate why the Dyad-4PNO model of Kern and Culpepper (2020) can be expected to fit real data reasonably well. The main result is that the Dyad-4PNO approximates a latent tree model. We offer a simple proof of identifiability, and draw some implications for psychological measurement in practice.

A Survey on Latent Tree Models and Applications

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summarize key ideas underlying the model. Second we explain how it can be efficiently learned from data. Third we illustrate its use within three types of applications: latent structure discovery, multidimensional clustering, and probabilistic inference. Finally, we conclude and give promising directions for future researches in this field.

Latent Tree Models and Approximate Inference in Bayesian Networks

We propose a novel method for approximate inference in Bayesian networks (BNs). The idea is to sample data from a BN, learn a latent tree model (LTM) from the data offline, and when online, make inference with the LTM instead of the original BN. Because LTMs are tree-structured, inference takes linear time. In the meantime, they can represent complex relationship among leaf nodes and hence the approximation accuracy is often good. Empirical evidence shows that our method can achieve good approximation accuracy at low online computational cost.