1 michel tenenhaus & carlo lauro a sem approach for composite indicators building michel...
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1
A SEM approach for composite indicators building
Michel Tenenhaus & Carlo LauroMichel Tenenhaus & Carlo Lauro
2
Economic inequality and political instability Data from Russett (1964), in GIFI
Economic inequalityAgricultural inequality
GINI : Inequality of land distributions
FARM : % farmers that own half of the land (> 50)
RENT : % farmers that rent all their land
Industrial developmentGNPR : Gross national product per
capita ($ 1955)
LABO : % of labor force employed in agriculture
Political instabilityINST : Instability of executive
(45-61)
ECKS : Nb of violent internal war incidents (46-61)
DEATH : Nb of people killed as a result of civic group violence (50-62)
D-STAB : Stable democracy
D-UNST : Unstable democracy
DICT : Dictatorship
3
Economic inequality and political instability (Data from Russett, 1964)
47 countries
4
GINI
FARM
RENT
GNPR
LABO
Agricultural inequality (X1)
Industrialdevelopment (X2)
ECKS
DEATH
INST
Politicalinstability (X3)
1
2
3
++
+
+
-
+
+
+
+
-
Economic inequality and political instability
5
Building composite indicators
1. Separately for each block (without taking into account the other blocks).
2. For each block, taking into account all the other blocks (multi-block data analysis).
3. For each block, taking into account the causal model (Structural Equation Modelling).
6
1
Politicalinstability
deathe31
eckse21
inste11
1. Using SEM for factor analysis
Measurement model
1
2
3
1
2
3
1
2
3
0 0
0 0
0 0
xΘ
1
2
3
xΛ
7
ULS algorithm
S = Observed covariance matrix for MV
2'
2
ˆ ˆ ˆ( )1GFI
x x εS Λ Λ Θ
S
Goodness-of-fit Index (Jöreskog & Sorbum):
2'
,
Minimize ( ) x ε
x x εΛ Θ
S Λ Λ Θ = PCA when 0εΘ
8
First result
1.00
Politicalinstability
death
.82
e31
ecks
-1.43
e21.551
.40
GFI=1.000
inst
.94
e1.21
1
This solution is not admissible because 2 2
ˆ ( ) 1.43Var e
9
A solution
The variance of residual e2 is fixed to a small value
2 2
ˆ ( ) .05Var e
1
Politicalinstability
deathe31
ecks
.05
e21
inste11
10
Result 2
The variance of residual e2 is fixed to a small value: 2 2
ˆ ( ) .05Var e
1.00
Politicalinstability
death
.61
e31
ecks
.05
e2.981
.60
GFI=.994
inst
.90
e1.27
1
11
Bootstrap ResultsRegression Weights:
Composite indicator
*Political instability i iX
12
Principal component analysis with SEM
The variance of the residuals are fixed to 0 : ˆ ( ) 0i iVar e
1
Politicalinstability
death
0
e31
ecks
0
e21
inst
0
e11
13
Result 3
The variance of the residuals are fixed to 0 : ˆ ( ) 0i iVar e
1.00
Politicalinstability
death
.00
e31
ecks
.00
e2.901
.81
GFI=.758
inst
.00
e1.49
1
14
Bootstrap Results
Regression Weights:
Conclusion
Coefficient of INST is not significant.
Parameter Estimate Lower Upper P Ecks <--- Political instability .900 .614 1.034 .010 Death <--- Political instability .813 .490 1.028 .010 Inst <--- Political instability .487 -.013 .996 .112
15
Result 4
The variance of the residuals are fixed to 0 : ˆ ( ) 0i iVar e
1.00
Politicalinstability
death
.00
e2
ecks
.00
e1
GFI=.950
1
1
.89
.89
16
Bootstrap ResultsRegression Weights:
Composite indicator
Political instability Ecks + Death
Parameter Estimate Lower Upper P Ecks <--- Political_instability .892 .665 1.045 .010 Death <--- Political_instability .892 .665 1.059 .010
17
2. Using SEM for multi-block data analysis
1
Agriculturalinequality
gini
e1
1
farm
e2
1
rent
e3
1
1
Industrialdeveloment
gnpr
e4
1
labo
e5
1
1
Politicalinstability
death
e8
1
ecks
e7
1
inst
e6
1
18
Result 5
1.00
Agriculturalinequality
gini
.21
e1
.87
1
farm
-.12
e2
1.05
1
rent
.79
e3
.44
1
1.00
Industrialdeveloment
gnpr
.12
e4
.93
1
labo
.24
e5
-.86
1
1.00
Politicalinstability
death
.44
e8
1
ecks
.28
e7
.84
1
-.39
.74
GFI=.868
inst
.28
.90
e6
1
.40 -.71
This solution is notadmissible because
2 2
ˆ ( ) .12Var e
19
Result 6
Var(e2) is fixedto a small value
2 2
ˆ ( ) .05Var e
1.00
Agriculturalinequality
gini
.10
e1
.94
1
farm
.05
e2
.99
1
rent
.82
e3
.40
1
1.00
Industrialdeveloment
gnpr
.10
e4
.94
1
labo
.25
e5
-.85
1
1.00
Politicalinstability
death
.34
e8
1
ecks
.40
e7
.76
1
-.31
.80
GFI=.978
inst
.27
.91
e6
1
.50 -.73
20
Result 7
MacDonald (1996)proposal
All Var(e) are fixedto 0:
ˆ ( ) 0i iVar e
1.00
Agriculturalinequality
gini
.00
e1
.95
1
farm
.00
e2
.98
1
rent
.00
e3
.57
1
1.00
Industrialdeveloment
gnpr
.00
e4
.96
1
labo
.00
e5
-.93
1
1.00
Politicalinstability
death
.00
e8
1
ecks
.00
e7
.87
1
-.26
.88
GFI=.888
inst
.39
.00
e6
1
.41 -.60
21
Bootstrap ResultsRegression Weights:
Parameter Estimate Lower Upper P Gini <--- Agricultural inequality .947 .800 1.052 .010 Farm <--- Agricultural inequality .979 .813 1.089 .010 Rent <--- Agricultural inequality .566 .053 .909 .051 Gnpr <--- Industrial develoment .957 .807 1.076 .010 Labo <--- Industrial develoment -.928 -1.052 -.739 .010 Ecks <--- Political instability .875 .624 1.038 .010 Death <--- Political instability .883 .642 1.044 .010 Inst <--- Political instability .395 -.019 .788 .115
Conclusion
Coefficient of INST is not significant.
22
Result 8MacDonald (1996)Proposals:
(1) All Var(e) are fixed to 0:
ˆ ( ) 0i iVar e
1.00
Agriculturalinequality
gini
.00
e1
.95
1
farm
.00
e2
.98
1
rent
.00
e3
.57
1
1.00
Industrialdeveloment
gnpr
.00
e4
.96
1
labo
.00
e5
-.92
1
1.00
Politicalinstability
death
.00
e8
1
ecks
.00
e7
.87
1
-.27
.92
GFI=.933
.42 -.60
(2) Composite indicator:
Political instability
.87*Ecks +.92*Death
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3. Causal model estimation using SEM-ULS
Agriculturalinequality
gini
e1
1
1
farm
e2
1
rent
e3
1
Industrialdevelopment
gnpr
e4
1
1
labo
e5
1
Politicalinstability
death
e8
1
ecks
e7
1
d11
1
inst
e6
1
24
Result 9
This solution is notadmissible because
2 2
ˆ ( ) .09Var e
.83
Agriculturalinequality
gini
.15
e1
1.00
1
farm
-.09
e2
1.14
1
rent
.82
e3
.43
1
.88
Industrialdevelopment
gnpr
.10
e4
1.00
1
labo
.25
e5
-.91
1
Politicalinstability
death
.34
e8
1
ecks
.40
e7
.95
1
-.26
.25
d11
1.00
GFI=.979
-.55.26
inst
.34
.91
e6
1
25
Result 10
Var(e2) is fixedto a small value
2 2
ˆ ( ) .05Var e
.88
Agriculturalinequality
gini
.10
e1
1.00
1
farm
.05
e2
1.05
1
rent
.82
e3
.42
1
.88
Industrialdevelopment
gnpr
.10
e4
1.00
1
labo
.25
e5
-.91
1
Politicalinstability
death
.34
e8
1
ecks
.40
e7
.95
1
-.27
.25
d11
1.00
GFI=.978
-.54.25
inst
.34
.91
e6
1
26
Bootstrap ResultsRegression Weights:
Conclusion
Coefficient of INST is not significant.
Parameter Estimate Lower Upper P Political instability <--- Industrial development -.544 -.792 -.371 .010 Political instability <--- Agricultural inequality .254 .057 .451 .031 Gini <--- Agricultural inequality 1.000 1.000 1.000 ... Farm <--- Agricultural inequality 1.053 .937 1.190 .010 Rent <--- Agricultural inequality .423 .047 .735 .051 Gnpr <--- Industrial development 1.000 1.000 1.000 ... Labo <--- Industrial development -.911 -1.215 -.685 .010 Ecks <--- Political instability .952 .594 1.405 .010 Death <--- Political instability 1.000 1.000 1.000 ... Inst <--- Political instability .337 -.029 .662 .130
27
Result 11
Var(e2) is fixedto a small value
2 2
ˆ ( ) .05Var e
Compositeindicator:
Political instability
.89*Ecks + 1.00*Death
.87
Agriculturalinequality
gini
.10
e1
1.00
1
farm
.05
e2
1.06
1
rent
.82
e3
.42
1
.90
Industrialdevelopment
gnpr
.07
e4
1.00
1
labo
.27
e5
-.88
1
Politicalinstability
death
.29
e8
1
ecks
.43
e7
.89
1
-.28
.28
d11
1.00
GFI=.982
-.55.26
28
Bootstrap ResultsRegression Weights:
Conclusion
All coefficients are significant.
Parameter Estimate Lower Upper P Political_instability <--- Industrial_development -.545 -.807 -.369 .010 Political_instability <--- Agricultural_inequality .265 .063 .449 .015 Gini <--- Agricultural_inequality 1.000 1.000 1.000 ... Farm <--- Agricultural_inequality 1.055 .939 1.194 .010 Rent <--- Agricultural_inequality .423 .044 .717 .051 Gnpr <--- Industrial_development 1.000 1.000 1.000 ... Labo <--- Industrial_development -.882 -1.189 -.680 .010 Ecks <--- Political_instability .892 .554 1.312 .010 Death <--- Political_instability 1.000 1.000 1.000 ...
29
Conclusion
• Agricultural inequality and Industrial development are drivers of political instability
• Russet hypotheses are validated:
• Other composite indicators:
2
Political instability .26*Agricultural inequality - .55*Industrial development
(p = .015) (p = .01)
R .596
Agricultural inequality 1.00*Gini + 1.06*Farm + .42*Rent
Industrial development 1.00*GNPR - .88*Labo
30
31
Conclusion
• Agricultural inequality above the average
• Industrial development below the average
DICTATORSHIP
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