Environmental Engineering Reference
In-Depth Information
Table 2. Variables listed in order of first CICA
component loading - magnitude of absolute value
- and subsequent order of loading in components
2 and 3. The first component is dominated by
stressor linked to air and water quality
Table 3. First component CICA loadings vs.
PCA loadings for ESI. Air and water effluent,
and treaty membership dominate the first com-
ponent. Conversely, the first PCA component is
less cohesive. The CICA loadings - the first order
determinants of the ESI - suggest that the major
drivers of sustainability are pollution (air and
water) and capacity
Variable
Name
Component
1
Component
2
Component
3
SO2
1
33
54
NO2
2
24
42
CICA
PCA
TSP
3
16
33
SO2
NUKE
ISO14
4
43
35
NO2
BODWAT
WATCAP
5
43
35
TSP
TFR
IUCN
6
23
25
ISO14
FSHCAT
CO2GDP
7
52
61
WATCAP
PESTHA
IUCN
WATSUP
CO2GDP
GRAFT
The factor loadings [Wherry1984] - the coef-
ficient weights the CICA rotation assigns to the
variables of the ESI - allude to the importance of
air quality in the first independent component, at
least, in concert with water quality, childhood
mortality and level of economic subsidy. This is
illustrated in the list of variables with the greatest
loadings or coefficient weights, in table 2.
The collection of traditional `stock' and non-
traditional `social capacity' variables in the first
three CICA components is interesting, especially
so when contrasted with the loadings generated
by PCA alone. The variables identified by the
CICA method offer a more coherent illustration
of the drivers of variation in the ESI; the diver-
gence in the CICA factors from the PCA one is a
proxy for the additional, non-Gaussian, informa-
tion or variability in the ESI. This difference is
due to the ability of the CICA algorithm to capture
dependence information in the data beyond mul-
tivariate normality. Table 3 lists the CICA loadings
vs. the PCA loadings for the first component.
THE FUTURE FOR
(ENVIRONMENTAL) INDEXING
Any index is essentially a - linear or non-linear
- collection of (almost always) non-independent
variables for the purpose of projecting a multi-
dimensional concept onto a univariate scale of
comparison. The scale of comparison - the range
of the index - though arbitrary, is completely
determined by the scheme for index construction
and the characteristics of the underlying data. A
useful index must be thoughtfully constructed;
consumers of the index, perhaps intuitively, typi-
cally focus on relative rankings rather than abso-
lute score. This is certainly true for development
indices - where relative performance can drive
international aid.
In a direct sense, the projection of the multivari-
ate data onto the univariate scale is the definition
of the index. When this projection is well known
or easily predictable, the scheme for construction
is straightforward: construct the index, i.e. weight
the variables, to minimize a loss between the index
and its predictable value.
