Page 206 - Becoming Metric Wise

196 Becoming Metric-Wise

the JDIF. Hence JDIF j ( j 5 1,2) denotes the diachronous impact factor
calculated exclusively with respect to pool j. Then we have the following
simple decomposition:

s1n21 CIT 1 ðY; Y 1 kÞ 1 s1n21
P P
s k5s k5s CIT 2 ðY; Y 1 kÞ
JDIF ðYÞ 5
n
PUBðYÞ
s s
5 JDIF ðYÞ 1 JDIF ðYÞ
n;1 n;2
(6.21)
because the pools are disjoint.
Clearly, if the global pool is subdivided into m disjoint subpools then
the decomposition takes the following form:
m
X
s
s
DIF ðYÞ 5 DIF ðYÞ: (6.22)
n n;j
j51
What happens if we have m possibly overlapping pools, as in the case
of JCR’s journal categories?
A citing journal may belong to 1, 2, .. ., m pools, making the situation
difficult to oversee. For two overlapping pools the answer is relatively
easy:

DIFðYÞ 5 DIF 1 ðYÞ 1 DIF 2 ðYÞ 2 DIF 1;2 ðYÞ (6.23)
where, to simplify the notation, we have omitted the length of the
citation window (n) and the offset period (s). The index 1,2 refers to
the journals in the intersection of pool 1 and pool 2. For the general
case (m possibly overlapping pools) we refer the reader to Rousseau
(2005b).

6.20.2 A Property of the Basic Journal Citation Model
Next we prove that in the basic journal citation model, explained below,
the 3-year synchronous impact factor is always larger than the 2-year JIF.
This calculation is taken from Rousseau et al. (2001).
It is generally agreed that synchronous citation curves are unimodal
graphs, having a mode at the year two or later. This is in accordance with
Price’s theory on the immediacy effect (Price, 1970). At the mode the
curve levels off, so that c(3) is larger than the average of c(1) and c(2),
where we denoted the number of citations given in year Y to documents