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

ABSTRACT

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.

KEYWORDS:

• Quantile regression
• spatial methods
• Bayesian methods
• count data
• foster care

Acknowledgements

We would like to thank Dr. Duncan Lee for generously sharing his code associated with the model used in [18] and Dr. J.M. Santos Silva for promptly and courteously answering a question we posed regarding [22]. Both of these interactions were instrumental in the completion of our process.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The authors would like to acknowledge that the abstract for this work was accepted for inclusion in the 2017 Joint Statistical Meetings (JSM) in Baltimore, Maryland. However, due to unforeseen personal circumstances, that presentation was canceled by the presenter in advance of the conference. As such, this information was not presented at those meetings and is instead on the program for JSM 2018 in Vancouver, British Columbia.