Page 244 - Becoming Metric Wise

235
Indicators

7.11.3 Final Comments on Time Series
Clearly many more time series are possible, but we think these are the
most interesting ones. In any case it must be made clear which type of
time series is used in an investigation. Time series are used to study the
dynamics of citation analysis, revealing trends and fluctuations. An inter-
esting research question is to find the underlying mechanism that
produces them. Such series may lead to (careful) predictions and hence
can also be used in forecasting. This aspect is interesting in the framework
of research evaluation: how will a scientist or research group most likely
perform in the future?
A formal description of these time series is provided in Liu &
Rousseau (2008), based on the notation introduced for impact factors in
Frandsen & Rousseau (2005) see Subsection 6.6.1.

7.12 THE OUTGROW INDEX (CR INDEX)
AND RELATED INDICES
7.12.1 Definitions

The outgrow or CR (citations of references) index was introduced by
Rousseau and Hu (2010). It is defined as follows. Consider an article
citation network and focus on one specific target article: the ego, as it is
called in network theory (Wasserman & Faust, 1994). Let A denote this
target article and consider A’s reference list, denoted as Ref(A). The length
of A’s reference list, i.e., its number of references, is denoted as TRef(A).
Article A and all articles in its reference list form a set, denoted as ER
(A) 5 Ref(A) , {A}, where ER stands for the extended reference list.
With each element of ER(A) we associate a positive number, and this in
different ways, leading to a family of indicators. These numbers lead to a
ranking of the members ER(A). The point is not so much this ranking
(although interesting in its own right) but the position of article A in this
ranked list.
As a first case we determine for each element of ER(A) the number of
articles by which it is cited. Next we rank all elements in ER(A) accord-
ing to its number of received citations. Finally the position of A in this
list is characterized by its citations-of-references, or outgrow index
defined as:

RðAÞ
CRðAÞ 5 1 2 (7.19)
TRef ðAÞ 1 1