Bayesian adjustment for measurement error in an offset variable in a Poisson regression model

Zhang, K; Liu, J; Liu, Y; Zhang, P; Carroll, RJ

Bayesian adjustment for measurement error in an offset variable in a Poisson regression model

Zhang, K Liu, J Liu, Y Zhang, P Carroll, RJ

Permalink

Publisher:: SAGE Publications
Publication Type:: Journal Article
Citation:: Statistical Modelling, 2021, pp. 1471082x2110080
Issue Date:: 2021-05-24

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Published versionAdobe PDF (959.45 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Zhang, K
dc.contributor.author	Liu, J
dc.contributor.author	Liu, Y
dc.contributor.author	Zhang, P
dc.contributor.author	Carroll, RJ
dc.date.accessioned	2022-01-14T01:40:02Z
dc.date.available	2022-01-14T01:40:02Z
dc.date.issued	2021-05-24
dc.identifier.citation	Statistical Modelling, 2021, pp. 1471082x2110080
dc.identifier.issn	1471-082X
dc.identifier.issn	1477-0342
dc.identifier.uri	http://hdl.handle.net/10453/153099
dc.description.abstract	<jats:p> Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL. </jats:p>
dc.language	en
dc.publisher	SAGE Publications
dc.relation.ispartof	Statistical Modelling
dc.relation.isbasedon	10.1177/1471082x211008011
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0104 Statistics, 1403 Econometrics
dc.subject.classification	Statistics & Probability
dc.title	Bayesian adjustment for measurement error in an offset variable in a Poisson regression model
dc.type	Journal Article
utslib.for	0104 Statistics
utslib.for	1403 Econometrics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access	*
dc.date.updated	2022-01-14T01:40:01Z
pubs.publication-status	Published online

Abstract:

Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/153099