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 sub-fields 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. The results with a fractional approach are very similar indeed.
normalization web of science categories citation analysis journal classification research performance european paradox