EC Research on Composite Indicators with Special Focus on ...
Transcript of EC Research on Composite Indicators with Special Focus on ...
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
EC Research on Composite Indicators with SpecialFocus on Missing Values
Ralf Munnich
Department of Statistics, Econometrics, and Operations ResearchUniversity of Tubingen
SECOND WORKSHOP ON COMPOSITE INDICATORS OFCOUNTRY PERFORMANCE
OECD Paris, 26. February 2004
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
EC Research on Composite Indicatorswith Special Focus on Missing Values
Outline of the PresentationOverview to the KEI ProjectMissing Values and Multiple ImputationA Case Study on a Composite IndicatorSummary and Outlook
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Knowledge Economy Indicators:Development of Innovative and Reliable Indicator Systems
KEI will focus on indicators and composite indicatorsReview of state-of-the-art methodologyMain thematic areas in relation to Lisbon and BarcelonaobjectivesIdentification of gaps
Development of innovative approachesAppropriate statistical methodologyMulti-criteria methodsAggregation and weighting techniquesElaboration of sensitivity analysisEvaluation of analytical properties of indicatorsInvestigation of adequate presentational techniquesSupport by large-scale simulation studyScenario analysis in co-operation with Commission services
−→ Policy-orientated research (FP6)
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Some Important Tasks of the Project
Five workshops with special focuses
Special topicsInvited and contributed paper presentations
Interest in co-operation with other projects / researchers inthe KEI area
Exchange of information via KEInews and WEB page
Contribution to journals and Commission publication(e.g. Statistics in Focus)
Final reports
Overview to KEI achievementsDetailed workpackage reportsPolicy analysis of knowledge economy indicators
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Structure of the Project
Defining the Knowledge-Based Economy
Indicators for the KBE
Statistical Analysis for KBE Indicators:
Mathematical and statistical properties of indicatorsData quality including missing value analysis
The Way Forward: Innovative Use of KBE Indicators
Composite Indicators for the KBE
Role of Multinationals for Information on R & D
Simulation Study:
Investigation of outcomes via simulation studyScenario analysis
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Partners of KEI
Eberhard Karls University of Tubingen: Ralf Munnich (CO)
Joint Research Center, Ispra: Andrea Saltelli
Katholieke Universiteit Leuven: Tom van Puyenbroeck
University of Maastricht, MERIT: Anthony Arundel
Statistics Finland: Mikael Akerblom
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Some aspects of Tubingen work
7 aspects of data quality (report) from Eurostat:relevance, accuracy, timeliness, accessability and clarity ofinformation, comparability, coherence, and completeness
Elaboration of data sourcesAnalysis based on Eurostat data quality workInvestigation of peculiarities and their influence on indicatorsRecommendations for choice of data sources
Recommended practices of methodology
Tools for indicator values computationOpen Source: R, cf. http://www.r-project.orgMicrosoft Excel c©Mathworks MatLab c©
Missing value analysis and their compensation−→ Imputation methodology
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Example for Missing Values in IndicatorsGERD PhD FTE GFCF EGov TEE LLL POP POP1
BDKDELEFIRLILNLAPFINSUK
BGCYCZEEHULTLVMTPLROSISKTR
USJP
0 1 2 3 4 5 6 7 8
Indicators for theknowledge-based economy
Number of missing values between1995 to 2002 with respect tocountry and indicator:
cf. DG RTD:Key Figures 2003 – 2004
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
The Multiple Imputation Principle (1)
NA
NA
NANA
Y1 Y2 Y3
Y1 Y2 Y31
1
11
Y1 Y2 Y32
2
22
Y1 Y2 Y33
3
33
Estimate 3
Estimate 2
Estimate 1
MI estimate
MI inference
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
The Multiple Imputation Principle (2)
Completedata
Incompletedata
Imputeddata set 1 θ(1) , var
(θ(1)
)
Imputeddata set 2 θ(2) , var
(θ(2)
)
Imputeddata set m θ(m) , var
(θ(m)
)
θ , var(θ)
missingvalues
θMI
varMI
(θ)
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
The Multiple Imputation Principle (3)
MI Estimates: Rubin (1978, 1987), or Barnard and Rubin (1999)
(θ − θ)/√
var(θ) ∼ N(0, 1)
Produce m completed data sets and calculate θ(j), var(θ(j))
θMI =1
m
m∑j=1
θ(j)
MI inference: Its estimated total variance is
var(θ) = varW(θ) +(1 +
1
m
)· varB(θ) with
varW(θ) =1
m
m∑j=1
var(θ(j)) and varB(θ) =
m∑j=1
(θ(j) − θMI )2
m − 1
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
First KEI-Imputation Based on PAN (1)
Research by Rassler and Munnich
Assume indicators are missing at random (MAR), Rubin andLittle (1987, 2002)
Fit univariate mixed-effects model for each KEI indicatorseparately (S-PLUS library PAN by Schafer 1997):
yc = Xcβ + Zcbc + εc , c = 1, 2, . . . ,C
Indicators yc = (yc1, yc2, . . . , ycT )′ for country cTime Xc with time interceptIntercept Zc
Fixed effects β0, β1
Random effects bc ∼ N(0, ψ) random effect for country cRandom errors εc ∼ NT (0, σ2 · IT )
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
First KEI-Imputation Based on PAN (2)
Generate m = 30 imputations after a burn-in period of 2000Gibbs cycles.
ACFs of ψ, σ2 and β suggest quick convergence
Lags of 1000 between each imputation are used
To do:
allow correlation between indicators ⇒ PAN for KEI accordingto Schafer & Yucel (2002)heteroscedasticity ⇒ possibly with Schafer & Yucel (2002)flexible serial correlation ⇒ future researchspacial autocorrelation ⇒ future research
Implementation in KEI with recommendations on modelling
Elaboration of accuracy with different models
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator on the Knowledge-based Economy (1)
Countries: EU15 + accession countries + USA + Japan
Time period: 1995 . . . 2002, early estimates for 2003
Indicators:
GERD Gross domestic expenditure for R & D per capita (POP)PhD Total new science and technology PhDs per capitaFTE Total researchers (FTE) per capitaGFCF Total gross fixed capital formation (excl. building) per
capitaEGov E-governmentTEE Total education expenditure per capitaLLL Life-long learning (per population aged 25-64 years par-
ticipating in education and training; POP1)
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator on the Knowledge-based Economy (2)
The seven single indicators will be denoted by y ti ;c with i for
indicator i , c for country c and t for year t.
Computation of z-scores for country c with given indicator iand time t with respect to t0 = 1995:
y ti ;c =
y ti ;c −
115
∑j∈EU15
y ti ;j√
115
∑j∈EU15
(y t0i ;j −
115
∑k∈EU15
y t0i ;k
)2=
y ti ;c −mean y1995
EU15
stdv y1995EU15
Special weighted average used to calculate z-scores
Translation term ignored
EU-14 instead of EU-15 (NA problem in Luxembourg)
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator on the Knowledge-based Economy (3)
The composite indicator I tc for country c and time t is then
I tc =
7∑i=1
λi · y ti ;c
with∑
i λi = 1 and
ytc =
(GERD
POP;PhD
POP;FTE
POP;GFCF
POP;EGov
1;TEE
POP;
LLL
POP1
),
λ =1
24·(2; 4; 2; 3; 3; 7; 3
).
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator on the Knowledge-based Economy (4)
1995 1996 1997 1998 1999 2000 2001 2002 2003B 3.7229 4.2197 4.2558 3.8697 4.1502 3.9287 5.0848 6.5412 7.8810DK 4.4973 4.5743 4.9003 5.3064 5.4270 5.8365 5.5205 4.8756 4.9856D 3.4558 3.3426 3.4559 3.5769 3.6986 3.8722 3.8699 4.1903 4.9375EL 1.1455 1.4450 1.4231 1.7580 1.7208 2.7858 2.7703 4.0024 4.8640E 2.0512 2.2117 2.3207 2.4624 2.6718 2.9120 3.3364 4.2854 4.8839F 3.5089 3.6056 3.6565 3.7244 3.9126 4.2079 4.3223 4.1323 4.9318IRL 2.3519 2.6215 2.8568 3.5979 3.5963 3.9702 4.4014 4.2331 4.8635I 2.5876 2.6998 2.7050 2.8407 3.0141 3.1834 4.2111 4.4280 4.8621L 4.1828 4.2132 4.7945 4.6289 5.1160 5.0595 4.7066 5.2216 5.8232NL 3.1769 3.3517 3.4954 3.6411 3.8147 3.9463 4.1874 4.2134 4.9699A 3.4867 3.6121 3.8066 4.0851 4.1375 4.2995 4.2735 4.4929 4.7863P 1.9244 2.1549 2.2246 2.6384 2.6827 2.8818 3.3156 3.5184 4.7724FIN 3.7844 3.7742 4.0505 4.5224 4.6914 5.0878 5.0697 4.7786 4.8476S 4.3808 4.4973 4.9553 5.1871 5.5521 5.6386 6.4295 4.7105 4.8236UK 3.1845 3.5367 3.4323 3.4701 3.5333 3.7311 4.1013 4.4949 4.9030
US 3.4160 3.4985 4.0556 3.9666 4.1419 4.3980 4.5686 4.8137 5.3452JP 3.5608 3.8332 3.9618 4.1311 4.0200 4.1406 4.3014 4.0665 4.8702
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator on the Knowledge-based Economy (4)
1995 1996 1997 1998 1999 2000 2001 2002 2003B 3.7229 4.2197 4.2558 3.8697 4.1502 3.9287 5.0848 6.5412 7.8810DK 4.4973 4.5743 4.9003 5.3064 5.4270 5.8365 5.5205 4.8756 4.9856D 3.4558 3.3426 3.4559 3.5769 3.6986 3.8722 3.8699 4.1903 4.9375EL 1.1455 1.4450 1.4231 1.7580 1.7208 2.7858 2.7703 4.0024 4.8640E 2.0512 2.2117 2.3207 2.4624 2.6718 2.9120 3.3364 4.2854 4.8839F 3.5089 3.6056 3.6565 3.7244 3.9126 4.2079 4.3223 4.1323 4.9318IRL 2.3519 2.6215 2.8568 3.5979 3.5963 3.9702 4.4014 4.2331 4.8635I 2.5876 2.6998 2.7050 2.8407 3.0141 3.1834 4.2111 4.4280 4.8621L 4.1828 4.2132 4.7945 4.6289 5.1160 5.0595 4.7066 5.2216 5.8232NL 3.1769 3.3517 3.4954 3.6411 3.8147 3.9463 4.1874 4.2134 4.9699A 3.4867 3.6121 3.8066 4.0851 4.1375 4.2995 4.2735 4.4929 4.7863P 1.9244 2.1549 2.2246 2.6384 2.6827 2.8818 3.3156 3.5184 4.7724FIN 3.7844 3.7742 4.0505 4.5224 4.6914 5.0878 5.0697 4.7786 4.8476S 4.3808 4.4973 4.9553 5.1871 5.5521 5.6386 6.4295 4.7105 4.8236UK 3.1845 3.5367 3.4323 3.4701 3.5333 3.7311 4.1013 4.4949 4.9030
US 3.4160 3.4985 4.0556 3.9666 4.1419 4.3980 4.5686 4.8137 5.3452JP 3.5608 3.8332 3.9618 4.1311 4.0200 4.1406 4.3014 4.0665 4.8702
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator (1995)
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator (2000)
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator (2001)
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator (2002)
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Composite Indicator (2003)
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Rank of Indicator Value (1995)R
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Rank of Indicator Value (2000)R
ank
B DK D EL E F IRL I L NL A P FIN S UK US JP
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Rank of Indicator Value (2001)R
ank
B DK D EL E F IRL I L NL A P FIN S UK US JP
15
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Rank of Indicator Value (2002)R
ank
B DK D EL E F IRL I L NL A P FIN S UK US JP
15
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
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OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Rank of Indicator Value (2003)R
ank
B DK D EL E F IRL I L NL A P FIN S UK US JP
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Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
![Page 29: EC Research on Composite Indicators with Special Focus on ...](https://reader034.fdocuments.net/reader034/viewer/2022042421/625ff26b4529247f232b1255/html5/thumbnails/29.jpg)
OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Comparison of EU14 and EU15 ScalingEU15 EU14 EU15 EU14 EU15 EU14
I 1995c rk I 1995
c rk I 2000c rk I 2000
c rk I 2003c rk I 2003
c rkB 3.7229 13 3.8248 13 3.9287 7 4.0301 7 7.8810 17 8.0079 17DK 4.4973 17 4.6388 17 5.8365 17 6.0338 17 4.9856 14 5.0793 13D 3.4558 9 3.5238 9 3.8722 6 3.9398 6 4.9375 12 5.0295 12EL 1.1455 1 1.1699 1 2.7858 1 2.7988 1 4.8640 7 4.9714 8E 2.0512 3 2.1025 3 2.9120 3 2.9792 3 4.8839 9 4.9805 9F 3.5089 11 3.5826 10 4.2079 11 4.2958 11 4.9318 11 5.0171 11IRL 2.3519 4 2.4124 4 3.9702 9 4.0690 9 4.8635 6 4.9635 7I 2.5876 5 2.6701 5 3.1834 4 3.2862 4 4.8621 5 4.9551 6L 4.1828 15 4.2689 15 5.0595 14 5.1589 14 5.8232 16 5.9719 16NL 3.1769 6 3.2622 7 3.9463 8 4.0602 8 4.9699 13 5.0833 14A 3.4867 10 3.5892 11 4.2995 12 4.4129 12 4.7863 2 4.8877 2P 1.9244 2 1.9793 2 2.8818 2 2.9630 2 4.7724 1 4.8661 1FIN 3.7844 14 3.8869 14 5.0878 15 5.1752 15 4.8476 4 4.9511 5S 4.3808 16 4.4769 16 5.6386 16 5.7561 16 4.8236 3 4.9257 3UK 3.1845 7 3.2479 6 3.7311 5 3.8083 5 4.9030 10 4.9860 10US 3.4160 8 3.4648 8 4.3980 13 4.4432 13 5.3452 15 5.4021 15JP 3.5608 12 3.6345 12 4.1406 10 4.2288 10 4.8702 8 4.9475 4
σEU15 = (0.153; 0.034; 0.753; 0.288; 0.158; 0.308; 0.068)
σEU14 = (0.151; 0.036; 0.782; 0.285; 0.154; 0.288; 0.064)
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators
![Page 30: EC Research on Composite Indicators with Special Focus on ...](https://reader034.fdocuments.net/reader034/viewer/2022042421/625ff26b4529247f232b1255/html5/thumbnails/30.jpg)
OutlineOverview to the KEI Project
Missing Values and Multiple ImputationA Case Study on a Composite Indicator
Summary and Outlook
Eberhard Karls
UniversitatTubingen
Summary and Outlook
Missing values cause many problems
Possible exclusion of important indicatorsDelayed publication of composite indicators
Multiple imputation
Gain stable estimatesInferenceAchieve early estimates for indicators (timeliness)
Data quality has to be considered
Accuracy of estimates (sample based data)Coherence of indicator valuesAcceptance in politics
http://kei.publicstatistics.net
Paris, 26. February 2004 Ralf Munnich EC Research on Composite Indicators