Identification of discrete concentration graph models with one hidden binary variable

TL;DR

This paper establishes conditions for the identifiability of discrete graph models with one hidden binary variable, linking model topology to the full rank of the parametrization map, and characterizes where identifiability fails.

Contribution

It provides necessary and sufficient conditions for model identifiability based on graph topology, extending latent class models to include conditional associations.

Findings

Full rank conditions depend on graph topology

Characterization of parameter space where identifiability fails

Extension of latent class models with conditional associations

Abstract

Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class model to allow for conditional associations between the observable random variables. Since local identification corresponds to full rank of the parametrization map, we establish a necessary and sufficient condition for the rank to be full everywhere in the parameter space. The condition is based on the topology of the undirected graph associated to the model. For non-full rank models, the obtained characterization allows us to find the subset of the parameter space where the identifiability breaks down.