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May 2005 On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables
Paul Gustafson
Statist. Sci. 20(2): 111-140 (May 2005). DOI: 10.1214/088342305000000098

Abstract

When a candidate model for data is nonidentifiable, conventional wisdom dictates that the model must be simplified somehow so as to gain identifiability. We explore two scenarios involving mismeasured variables where, in fact, model expansion, as opposed to model contraction, might be used to obtain identifiability. We compare the merits of model contraction and model expansion. We also investigate whether it is necessarily a good idea to alter the model for the sake of identifiability. In particular, estimators obtained from identifiable models are compared to those obtained from nonidentifiable models in tandem with crude prior distributions. Both asymptotic theory and simulations with Markov chain Monte Carlo-based estimators are used to draw comparisons. A technical point which arises is that the asymptotic behavior of a posterior mean from a nonidentifiable model can be investigated using standard asymptotic theory, once the posterior mean is described in terms of the identifiable part of the model only.

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Paul Gustafson. "On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables." Statist. Sci. 20 (2) 111 - 140, May 2005. https://doi.org/10.1214/088342305000000098

Information

Published: May 2005
First available in Project Euclid: 14 July 2005

zbMATH: 1087.62037
MathSciNet: MR2183445
Digital Object Identifier: 10.1214/088342305000000098

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.20 • No. 2 • May 2005
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