Abstract
Bayesian quantile regression has drawn more attention in widespread applications recently. Yu and Moyeed (2001) proposed an asymmetric Laplace distribution to provide likelihood based mechanism for Bayesian inference of quantile regression models. In this work, the primary objective is to evaluate the performance of Bayesian quantile regression compared with simple regression and quantile regression through simulation and with application to a crime dataset from 50 USA states for assessing the effect of potential risk factors on the violent crime rate. This paper also explores improper priors, and conducts sensitivity analysis on the parameter estimates. The data analysis reveals that the percent of population that are single parents always has a significant positive influence on violent crimes occurrence, and Bayesian quantile regression provides more comprehensive statistical description of this association.
Highlights
Crime has been a major and long-standing issue in the United States
We consider one historical crime data appeared in Statistical Methods for Social Sciences by Agresti and Finlay (1997) to identity risk factors on violent crime rate, where the most interest covariates are the percent of population that are single parents and the percent of population living under poverty line [3]
Variable Label sid state id state state name crime violent crimes per 100,000 murder murders per 1,000,000 pctmetro the pct of the population living in metropolitan areas pctwhite pcths the percent of the population that is white the percent of population with a high school education or above poverty the percent of population living under poverty line single the percent of population that are single parents regression for comparison
Summary
Crime has been a major and long-standing issue in the United States. Since 1964, the US crime rate has increased by as high as 350% [1]. The overall crime rate is displayed in fifty states referring to the violent crime and the property crime in combination. There exist a lot of risk factors having great impact on crime rates in the Unites States. We consider one historical crime data appeared in Statistical Methods for Social Sciences by Agresti and Finlay (1997) to identity risk factors on violent crime rate, where the most interest covariates are the percent of population that are single parents and the percent of population living under poverty line [3]. We propose the combination of quantile regression and Bayesian method for comparison by simultaneously taking those advantages into account.
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