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Seemingly Unrelated Regression with Measurement Error: Estimation via Markov chain Monte Carlo and Mean Field Variational Bayes Approximation

Georges Bresson, Anoop Chaturvedi, Mohammad Arshad Rahman, Shalabh

arXiv 12 Jun 2020 · Statistics — Methodology · publishedThe International Journal of Biostatistics (2020) · 10 citations (OpenAlex)

arXiv:2006.07074 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates arising due to different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.

Citation extraction

46
references
76
in-text mentions
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distinct cited
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main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Owen, A. B (2017) Statistically Efficient Thinning of a Markov Chain Sampler0.92844100%
2Carroll, R. J., Midthune, D., Freedman, L. S., and Kipnis, V (2006) Seemingly Unrelated Measurement Error Models with Application to Nutritional Epidemiology0.87472100%
3Pham, T. H., Ormerod, J. T., and Wand, M. P (2013) Mean Field Variational Bayesian Inference for Nonparametric Regression with Measurement Error0.81142100%
4Zellner, A (1971) An Introduction to Bayesian Inference in Econometrics0.81142100%
5Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M (2006) Measurement Error in Nonlinear Models: A Modern Perspective0.64422100%
6Cheng, C.-L. and Van Ness, J. W (1999) Statistical Regression with Measurement Error0.64422100%
7Fuller, W. A (1987) Measurement Error Models0.64422100%
8Link, W. A. and Eaton, M. J (2012) On Thinning of Chains in MCMC0.64422100%
9Bishop, C. M (2006) Pattern Recognition and Machine Learning0.58531100%
10Blei, D. M., Kuckelbir, A., and McAuliffe, J. D (2017) Variational Inference: A Review for Statisticians0.58531100%

Showing the top 10 of 46 scored citations.