Deriving Complete Constraints in Hidden Variable Models

TL;DR

This paper introduces a systematic method for deriving all observable constraints in hidden variable models with categorical data, enhancing model testing and estimation accuracy.

Contribution

It provides a new approach to identify the complete set of observable constraints in certain hidden variable models, including both inequalities and equalities.

Findings

Derived constraints can falsify model assumptions.

Method applies to models with categorical variables and linear relations.

Includes new settings with inequality and equality constraints.

Abstract

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that would otherwise be untestable due to the unobserved variables and can be used to constrain estimation procedures to improve statistical efficiency. Knowing the complete set of observable constraints is thus ideal, but this can be difficult to determine in many settings. In models with categorical observed variables and a joint distribution that is completely characterized by linear relations to the unobservable response function variables, we develop a systematic method for deriving the complete set of observable constraints. We illustrate the method in several new settings, including ones that imply both inequality and equality constraints.