1. Data Analysis of Environmental Air Pollutant Monitoring Systems in Europe
Kristina Voigt, Gerhard Welzl, and Rainer Brüggemann
Environmetrics 2004; 15:
Multiple Indicators, Partially Ordered Sets, and Linear Extensions: Multi-criterion Ranking and Prioritization
G.P. Patil and Charles Taillie
Environmental and Ecological Statistics 2004; 11:

2. Evaluation Criteria and their Scores
Number of chemicals monitored/NU
Score
<4
5-7 1
>7 2
Types and duration of measurements/ME
Only daily values, yesterday’s values
daily + past week, past 2 weeks
daily + past weeks + past 6 months, past year(s)
Measurement stations in capital/ST
1-2
3-5
>6
Method of presentation on the Internet/PR
Table
Graphic
Table + Graphic
Background material/BM
Explanations, reports
+limit values, laws and regulations
direct communication, measures

3. 15 European Monitoring Stations Evaluated by 5 Criteria
Abb. NU ME ST PR BM
AUS 1 2
BEL
DEN
FIN
FRA
GER
GRE
IRE
ITA
LUX
NET
POR
SPA
SWE
UNK

4. Hasse Diagram for the EEC 15*5 Dataset
Abbr.
Rank of EEC5
FRA 1
GER 2
BEL 3
UNK 4
DEN 5
ITA 6
AUS 7
FIN 8
NET 9
POR
10.5
SWE
SPA 12
GRE 13
IRE 14
LUX 15

5. Hasse Diagram : Levels

6. Regions in the Coordinate Space of POSACY
(III) Region of points incomparable to P
(II) Region of points greater than P Yp P
(I) Region of points smaller than P
(III) Region of points incomparable to P Xp X

7. Two Profiles in a Cartesian Coordinate Space2
2,2,2,2,1
GER 2
2,2,2,2,1
GER Y Y 1
2,0,2,1,1
ITA
2,2,2,2,1
GER Y
2,0,2,1,1
ITA
2,0,2,1,1
ITA 1 1 1 1 2 1 2 X X X
For these possible score assignments are:
2,0,2,1,1  11 2,0,2,1,1  11 2,0,2,1,1  11
2,2,2,2,1  12 2,2,2,2,1  21 2,2,2,2,1  22

8. Three profiles in a two-dimensional coordinate spaceY 3
2,2,0,2,2 2
2,2,2,2,1 1
2,0,2,1,1 X 1 2 3

10. POSAC Output Proportion of profile pairs correctly represented: 0.926
Label DIM DIM Joint Lateral Fit
GER
FRA
BEL
DEN
AUS
FIN
UNK
ITA
NET
POR
SWE
GRE
IRE
SPA
LUX

11. PCA Output

14. PCA chooses 3 variables ME, ST, and PR
POSAC chooses 2 variables ST and PR
Abbr.
Rank of EEC5
ME,ST, PR
ST, PR
FRA 1
1.5
GER 2
BEL 3
3.5
UNK 4
7.5 6
DEN 5
8.5
ITA
AUS 7
FIN 8
NET 9
9.5
POR
10.5 12 11
SWE 14
SPA
GRE 13
IRE
14.5
LUX 15
CORRELATION

15. Hasse Diagram of 15*4 Dataset (Leaving out the attribute ST)
Abbr.
Rank of EEC5
-ST
FRA 1 3
GER 2
BEL
UNK 4
6.5
DEN 5
ITA 6
AUS 7
FIN 8
9.5
NET 9
POR
10.5
11.5
SWE
SPA 12 14
GRE 13
IRE
LUX 15
CORRELATION
0.912

16. Leave Out One Variable at a Time
Abbr.
Rank of EEC5
-NU
-ME
-ST
-PR
-BM
FRA 1 3 2
GER
BEL 4
6.5
UNK 8
DEN 5 7
5.5
ITA 6
AUS
7.5
FIN
9.5
NET 9 10
POR
10.5
11.5 12
SWE
13.5 11
SPA 14
GRE 13
IRE
14.5
LUX 15
CORRELATION
0.9678
0.972
0.891

17. Sub-graph of the Object GER in the Super-graphic

18. Evaluation of the W-matrix for All Elements

19. Comparison of Results in Hasse Diagrams with Different Attribute Sets

20. PCA Biplot of 15*5 Data Matrix

21. POSAC Plot of Data Matrix 15*5

22. Scatter Plots of the Variables ST and PR

23. Hasse Diagram of Reduced Data Matrix 15*2 (LOVs from POSAC)