Bayesian spatial quantile regression for areal count data, with application on substitute care placements in Texas

Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables and without considering spatial effects. Of the few studies that have perf...

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Bibliographic Details
Published in:Journal of applied statistics 2019-03, Vol.46 (4), p.580-597
Main Authors: King, Clay, Song, Joon Jin
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian methods
Computer simulation
Continuity (mathematics)
count data
foster care
Quantile regression
Regression analysis
spatial methods
Statistical methods
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Summary:Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables and without considering spatial effects. Of the few studies that have performed QR on count data, none have included random spatial effects, which is an integral facet of the Bayesian spatial QR model for areal counts that we propose. Additionally, we introduce a simplifying alternative to the response variable transformation currently employed in the QR for counts literature. The efficacy of the proposed model is demonstrated via simulation study and on a real data application from the Texas Department of Family and Protective Services (TDFPS). Our model outperforms a comparable non-spatial model in both instances, as evidenced by the deviance information criterion (DIC) and coverage probabilities. With the TDFPS data, we identify one of four covariates, along with the intercept, as having a nonconstant effect across the response distribution.
ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2018.1508557