Sub-field normalization in the multiplicative case: Average-based citation indicators

This paper investigates the citation impact of three large geographical areas -- the U.S., the European Union (EU), and the rest of the world (RW) -- at different aggregation levels. The difficulty is that 42% of the 3.6 million articles in our Thomson Scientific dataset are assigned to several sub-fields among a set of 219 Web of Science categories. We follow a multiplicative approach in which every article is wholly counted as many times as it appears at each aggregation level. We compute the crown indicator and the Mean Normalized Citation Score (MNCS) using for the first time sub-field normalization procedures for the multiplicative case. We also compute a third indicator that does not correct for differences in citation practices across sub-fields. It is found that: (1) No geographical area is systematically favored (or penalized) by any of the two normalized indicators. (2) According to the MNCS, only in six out of 80 disciplines -- but in none of 20 fields -- is the EU ahead of the U.S. In contrast, the normalized U.S./EU gap is greater than 20% in 44 disciplines, 13 fields, and for all sciences as a whole. The dominance of the EU over the RW is even greater. (3) The U.S. appears to devote relatively more -- and the RW less -- publication effort to subfields with a high mean citation rate, which explains why the U.S./EU and EU/RW gaps for all sciences as a whole increase by 4.5 and 5.6 percentage points in the un-normalized case.