Identification of discrete concentration graph models with one hidden binary variable

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 obs...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2013-11, Vol.19 (5A), p.1920-1937
Main Authors: STANGHELLINI, ELENA, VANTAGGI, BARBARA
Format: Article
Language:English
Subjects:
conditional independence
contingency tables
finite mixtures
Hidden variables
Identifiability
latent class
latent structure
log linear models
Mathematical independent variables
Mathematical vectors
Matrices
Parametric models
Random variables
Statism
Statistical models
Sufficient conditions
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Summary: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.
ISSN:1350-7265
DOI:10.3150/12-BEJ435