How do self-archiving and Author-pays models associate and contribute to OA citation advantage within hybrid journals

Hybrid open access journals generally authorize self-archiving along with Author-pays model. Given the dependence of the Author-pays model on APCs paid by authors, it is expected to have a negative association with the free-of-charge Green model. By exploring a sample of 52,150 papers published in 47 Elsevier's hybrid journals, the study compares the OA models' citation performances to non-open access (NOA) model's and investigates the relationship between the quantities of their papers. Three OA groups are identified, including Green-only, APC-only and Green-APC. The OA papers show a citation advantage over the NOA articles, despite their lower number. The mixed APC-Green, gains the highest citation compared to the three other access models. However, the number of Green and APC-funded papers are revealed to have a negative association. Although, the combination of the Green and APC models magnifies the impact of OA papers, the inverse association between the quantities of their papers signifies that the lower number of the latter can be partially explained by the prevalence of the former. The results help academic librarians involved in advocating and managing OA to better understand authors' behaviors towards OA models and adopt a more supportive role for OA according to their preferences.