A new algorithm for zero-modified models applied to citation counts

Abstract

Finding statistical models for citation count data is important for those seeking to understand the citing process or when using regression to identify factors that associate with citation rates. As sets of citation counts often include more or less zeros (uncited articles) than would be expected under the base distribution, it is essential to deal appropriately with them. This article proposes a new algorithm to fit zero-modified versions of discretised lognormal, hooked power-law and Weibull models to citation count data from 23 different Scopus categories from 2012. The new algorithm allows the standard errors of all parameter estimates to be calculated, and hence also confidence intervals and p-values. This algorithm can also estimate negative zero-modification parameters corresponding to zero-deflation (fewer uncited articles than expected). The results find no universal best model for the 23 categories. A given dataset may be zero-inflated relative to one model, but zero-deflated relative to another. We suggest circumstances in which one of the models under consideration may be the best fitting model.