Statistical Science

On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables

Paul Gustafson

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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.

Article information

Source
Statist. Sci. Volume 20, Number 2 (2005), 111-140.

Dates
First available in Project Euclid: 14 July 2005

Permanent link to this document
http://projecteuclid.org/euclid.ss/1121347636

Digital Object Identifier
doi:10.1214/088342305000000098

Mathematical Reviews number (MathSciNet)
MR2183445

Zentralblatt MATH identifier
1087.62037

Citation

Gustafson, Paul. On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables. Statist. Sci. 20 (2005), no. 2, 111--140. doi:10.1214/088342305000000098. http://projecteuclid.org/euclid.ss/1121347636.


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