An empirical review of the different variants of the probabilistic affinity index as applied to scientific collaboration

Responsible indicators are crucial for research assessment and monitoring. Transparency and accuracy of indicators are required to make research assessment fair and ensure reproducibility. However, sometimes it is difficult to conduct or replicate studies based on indicators due to the lack of transparency in conceptualization and operationalization. In this paper, we review the different variants of the Probabilistic Affinity Index (PAI), considering both the conceptual and empirical underpinnings. We begin with a review of the historical development of the indicator and the different alternatives proposed. To demonstrate the utility of the indicator, we demonstrate the application of PAI to identifying preferred partners in scientific collaboration. A streamlined procedure is provided, to demonstrate the variations and appropriate calculations. We then compare the results of implementation for 5 specific countries involved in international scientific collaboration. Despite the different proposals on its calculation, we do not observe large differences between the PAI variants, particularly with respect to country size. As with any indicator, the selection of a particular variant is dependent on the research question. To facilitate appropriate use, we provide recommendations for the use of the indicator given specific contexts.