A Bayesian two-part quantile regression model for count data with excess zeros

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 produced by a single data-generating process. Of the few studies that have performed QR on count data, none have accounted for excess zeros from a Bayesian perspective, as does the hurdle model that we propose. In this article, we propose a Bayesian two-part QR model for count data with excess zeros. The proposed model is compared to a frequentist approach via simulation, and its usefulness is displayed on two real datasets. In each application, multiple covariates are found to have differing effects across the response distribution, with special attention given to the nature of those effects in the outermost response distribution quantiles.

Bayesian Analysis of Nonnegative Data Using Dependency-Extended Two-Part Models

“…However, these authors did not assume any extension between the two parts. Bayesian models have also been proposed for zero-inflated longitudinal nonnegative data (Swallow et al 2016;Biswas and Das 2020) and zero-inflated count data (Neelon et al 2010;King and Song 2019;Bertoli et al 2020). Specifically, Biswas and Das (2020) and Neelon et al (2010) proposed models with correlated random effects, which in this regard are similar to our Model 1.…”

Application of a Hurdle Model with Random Effects to Explore the Relationship between Operational Characteristics and Safety Performance

“…These distributions assume that some zero observations happen by chance (where the entities are unsafe but happen to have zero crashes observed during the period of observation) and allocate a probability to observe zero counts. These zeros are referred to as ‘sampling zeros.’ The probability density function of a zero-inflated negative binomial (ZINB) model is given in Equation 2, which caters to zeros generated by the two different processes: (i) the process that generates structural zeros (zero-count state); and (ii) the process that generates sampling zeros from a NB distribution ( 25 , 26 , 33 ). where pit is the probability of entity i being a zero-count state in round t…”

“…These zeros are referred to as 'sampling zeros.' The probability density function of a zero-inflated negative binomial (ZINB) model is given in Equation 2, which caters to zeros generated by the two different processes: (i) the process that generates structural zeros (zero-count state); and (ii) the process that generates sampling zeros from a NB distribution (25,26,33).…”

A Bayesian hurdle quantile regression model for citation analysis with mass points at lower values

“…The approach proposed in this article is an extension of the Bayesian two-part Hurdle QR model of King and Song (2019). Having a two-part structure is a fundamental aspect of this model.…”

“…We focus on two challenges for citation count analysis by quantile regression: discontinuity and substantial mass points at lower counts. A Bayesian hurdle quantile regression model for count data with a substantial mass point at zero was proposed by King and Song (2019). It uses quantile regression for modeling the nonzero data and logistic regression for modeling the probability of zeros versus nonzeros.…”