Researchers’ academic output is frequently quantified by size and quality, and citation impact is frequently used as a proxy for quality. Bibliometric indicators of research output are often included in the periodical evaluations of researchers. In this article, we model the dependencies between several bibliometric indicators beyond the common correlation coefficients. We first investigate the behaviour of the correlation coefficients on different ranges of the distribution and emphasize the (lack) of tail dependence. Investigating the correlations for the division Social Sciences unveils intricate relationships between the indicators that emphasize the necessity of more sophisticated dependence modelling tools. We therefore propose copulas in order to account for complex dependency structures of pairs of indicators of 3574 researchers from Quebec. Bivariate parametric copulas that best fit the data are chosen and evaluated with respect to a goodness of fit test. Even though the performance of the parametric copulas is modest for the division Social Sciences, the methodology has an undoubtable merit and other parametric families or nonparametric copulas should definitely be further investigated.