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 () and Shalabh ()
Additional contact information
Shalabh: Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

The International Journal of Biostatistics, 2021, vol. 17, issue 1, 75-97

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 for 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.

Keywords: classical measurement error; Markov chain Monte Carlo (MCMC); mean field variational Bayes; reliability ratio; seemingly unrelated regression; systolic blood pressure (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/ijb-2019-0120 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
Working Paper: Seemingly Unrelated Regression with Measurement Error: Estimation via Markov chain Monte Carlo and Mean Field Variational Bayes Approximation (2020)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:17:y:2021:i:1:p:75-97:n:1

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/ijb/html

DOI: 10.1515/ijb-2019-0120

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().