A Bayesian Two-part Hurdle Quantile Regression Model for Citation Analysis

Quantile regression is a technique to analyse the effects of a set of independent variables on the entire distribution of a continuous response variable. Quantile regression presents a complete picture of the effects on the location, scale, and shape of the dependent variable at all points, not just at the mean. This research focuses on two challenges for the analysis of citation counts by quantile regression: discontinuity and substantial mass points at lower counts, such as zero, one, two, and three. A Bayesian two-part hurdle quantile regression model was proposed by King and Song (2019) as a suitable candidate for modeling count data with a substantial mass point at zero. Their model allows the zeros and non-zeros to be modeled independently but simultaneously. It uses quantile regression for modeling the nonzero data and logistic regression for modeling the probability of zeros versus nonzeros. Nevertheless, the current paper shows that substantial mass points also at one, two, and three for citation counts will nearly certainly affect the estimation of parameters in the quantile regression part of the model in a similar manner to the mass point at zero. We update the King and Song model by shifting the hurdle point from zero to three, past the main mass points. The new model delivers more accurate quantile regression for moderately to highly cited articles, and enables estimates of the extent to which factors influence the chances that an article will be low cited. To illustrate the advantage and potential of this method, it is applied separately to both simulated citation counts and also seven Scopus fields with collaboration, title length, and journal internationality as independent variables.