  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.
