A Mathematical Model of Academic Citation Age

Using citation data, this article examines the pattern of diffusion in the academic literatures of science, the social sciences, and the arts and humanities. An examination of the citations from a given year to the year in which the cited article was published shows that the initial level of citations starts out small and then increases, reaching a peak in less than two years. It then gradually decreases as articles age. A mathematical model is developed to describe this pattern, which is compared to a linear model. The model explains between 97.2% and 99.2% of the variance, depending on the data set, with the parameters for science and the social sciences being remarkably similar. Based on this model, we find that the age at which citation reaches a maximum is lowest for the arts and humanities, next for science, and last for the social sciences. The peak in the proportion of citations is greatest for science, followed by the social sciences and the arts and humanities. Problems in the model led to an examination of one source of historical change in citation practice. We find that the number of citations per article per year has increased systematically over time. Diffusion research is discussed in light of the utility of the citation model.

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