Transcript Ejemplo ‘raw data’ - Pompeu Fabra University

Example of EQS with
‘raw data’
Sintaxis generator
Method = robust
Multiple group
Mean and covariances (MACS)
Purpose …
• We have two samples with 162 clients, car retail sellers,
from Spain and 109 from USA
• For each client the percibed quality of service and the
loyalty to the car retailer
• 7 points likert scale for quality items.
• 5 points likert scale for Loyalty items.
• We want to research if perceived quality is related with
Loyalty, and whether the relation is the same in the two
countries.
Modelo
Q1
Q2
L1
Q3
L2
Q4
Calidad
Lealtad
L3
Q5
L4
Q6
L5
Q7
Modelo muestra española
/TITLE
modelo_espana
/SPECIFICATIONS
DATA='c:\eqs61\espa_auto.ess';
VARIABLES=12; CASES=162;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE;
MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 = 1F1 + E1;
V2 = *F1 + E2;
V3 = *F1 + E3;
V4 = *F1 + E4;
V5 = *F1 + E5;
V6 = *F1 + E6;
V7 = *F1 + E7;
V8 = 1F2 + E8;
V9 = *F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F2 = *F1 + D2;
/VARIANCES
F1 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E10 = *;
E11 = *;
E12 = *;
D2 = *;
/COVARIANCES
/PRINT
EIS;
FIT=ALL;
TABLE=EQUATION;
/END
Modelo muestra española
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE
INDEPENDENCE AIC =
MODEL AIC =
1600.22971
12.42112
=
1732.230 ON
INDEPENDENCE CAIC =
MODEL CAIC =
66 DEGREES OF FREEDOM
1331.26824
-203.56309
CHI-SQUARE =
118.421 BASED ON
53 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.932
BENTLER-BONETT NON-NORMED FIT INDEX =
.951
COMPARATIVE FIT INDEX (CFI)
=
.961
BOLLEN
(IFI) FIT INDEX
=
.961
MCDONALD (MFI) FIT INDEX
=
.815
LISREL
GFI FIT INDEX
=
.899
LISREL
AGFI FIT INDEX
=
.851
ROOT MEAN-SQUARE RESIDUAL (RMR)
=
.119
STANDARDIZED RMR
=
.041
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.067,
=
107.321.
.088
.109)
Non-normality
• When normality is violated, what are the
implications (robustness)?
– We tend to reject correct models more often
• χ2 is larger
– We tend to consider significative parameters
that in reality are not significant
• Inflate the precision of parameter estimates
Spanish sample
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
972.11041
-14.70039
1104.110 ON
INDEPENDENCE CAIC =
MODEL CAIC =
66 DEGREES OF FREEDOM
703.14894
-230.68461
SATORRA-BENTLER SCALED CHI-SQUARE =
91.2996 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
53 DEGREES OF FREEDOM
.00085
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
121.970
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
69.210
.06669
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
53,
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.917
BENTLER-BONETT NON-NORMED FIT INDEX =
.954
COMPARATIVE FIT INDEX (CFI)
=
.963
BOLLEN
(IFI) FIT INDEX
=
.964
MCDONALD (MFI) FIT INDEX
=
.887
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.043,
1.549
107
.02863
=
.067
.090)
… spanish sample(cnt.)
MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
Q1
=V1
=
1.000 F1
+ 1.000 E1
Q2
=V2
=
1.220*F1
.125
9.761@
.127)
9.644@
+ 1.000 E2
1.197*F1
.120
10.011@
(
.135)
( 8.856@
(
(
Q3
=V3
=
+ 1.000 E3
Q4
=V4
=
+ 1.000 E4
Q5
=V5
=
1.295*F1
.125
10.402@
(
.139)
( 9.346@
(
(
Q6
=V6
=
(
(
Q7
=V7
=
(
(
1.016*F1
.112
9.062@
.135)
7.551@
+ 1.000 E5
1.103*F1
.121
9.130@
.155)
7.101@
+ 1.000 E6
1.103*F1
.121
9.136@
.130)
8.471@
+ 1.000 E7
L1
=V8
=
1.000 F2
=
.786*F2
.079
9.933@
(
.066)
( 11.854@
+ 1.000 E8
L2
=V9
L3
=V10 =
+ 1.000 E10
L4
=V11 =
+ 1.000 E11
L5
=V12 =
+ 1.000 E12
1.051*F2
.053
19.683@
(
.046)
( 22.782@
1.078*F2
.053
20.415@
(
.047)
( 22.967@
1.056*F2
.064
16.585@
(
.052)
( 20.327@
+ 1.000 E9
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
F2
=F2
=
(
(
1.147*F1
.125
9.168@
.144)
7.943@
+ 1.000 D2
… spanish sample(cnt.)
STANDARDIZED SOLUTION:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
L1
L2
L3
L4
L5
F2
=V1
=V2
=V3
=V4
=V5
=V6
=V7
=V8
=V9
=V10
=V11
=V12
=F2
=
=
=
=
=
=
=
=
=
=
=
=
=
.686 F1
.836*F1
.860*F1
.898*F1
.771*F1
.777*F1
.777*F1
.928 F2
.650*F2
.907*F2
.918*F2
.852*F2
.829*F1
R-SQUARED
+
+
+
+
+
+
+
+
+
+
+
+
+
.728
.549
.511
.440
.637
.630
.629
.372
.760
.420
.396
.523
.559
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
D2
.470
.699
.739
.807
.594
.603
.604
.862
.423
.823
.843
.726
.688
USA sample
/TITLE
modelo_USA
/SPECIFICATIONS
DATA='c:\eqs61\usa_auto.ess';
VARIABLES=12; CASES=109;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE;
MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 = 1F1 + E1;
V2 = *F1 + E2;
V3 = *F1 + E3;
V4 = *F1 + E4;
V5 = *F1 + E5;
V6 = *F1 + E6;
V7 = *F1 + E7;
V8 = 1F2 + E8;
V9 = *F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F2 = *F1 + D2;
/VARIANCES
F1 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E10 = *;
E11 = *;
E12 = *;
D2 = *;
/COVARIANCES
/PRINT
EIS;
FIT=ALL;
TABLE=EQUATION;
/END
USA sample (cnt.)
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE
INDEPENDENCE AIC =
MODEL AIC =
1325.24370
8.17449
=
1457.244 ON
INDEPENDENCE CAIC =
MODEL CAIC =
66 DEGREES OF FREEDOM
1083.45672
-185.98778
CHI-SQUARE =
114.174 BASED ON
53 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.922
BENTLER-BONETT NON-NORMED FIT INDEX =
.945
COMPARATIVE FIT INDEX (CFI)
=
.956
BOLLEN
(IFI) FIT INDEX
=
.956
MCDONALD (MFI) FIT INDEX
=
.749
LISREL
GFI FIT INDEX
=
.857
LISREL
AGFI FIT INDEX
=
.789
ROOT MEAN-SQUARE RESIDUAL (RMR)
=
.098
STANDARDIZED RMR
=
.037
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.078,
=
105.399.
.105
.130)
USA sample (cnt.)
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
652.46267
-35.78090
784.463 ON
INDEPENDENCE CAIC =
MODEL CAIC =
66 DEGREES OF FREEDOM
410.67569
-229.94317
SATORRA-BENTLER SCALED CHI-SQUARE =
70.2191 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
53 DEGREES OF FREEDOM
.05675
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
150.778
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
62.242
.18031
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
53,
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.910
BENTLER-BONETT NON-NORMED FIT INDEX =
.970
COMPARATIVE FIT INDEX (CFI)
=
.976
BOLLEN
(IFI) FIT INDEX
=
.976
MCDONALD (MFI) FIT INDEX
=
.922
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.000,
1.436
53
.09554
=
.056
.088)
USA sample (cnt.)
MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
Q1
=V1
=
1.000 F1
+ 1.000 E1
Q2
=V2
=
.895*F1
.129
6.940@
.118)
7.594@
+ 1.000 E2
1.072*F1
.125
8.578@
.126)
8.518@
+ 1.000 E3
1.132*F1
.128
8.853@
.117)
9.634@
+ 1.000 E4
.999*F1
.114
8.795@
.110)
9.052@
+ 1.000 E5
1.165*F1
.132
8.832@
.124)
9.416@
+ 1.000 E6
1.218*F1
.146
8.363@
.130)
9.349@
+ 1.000 E7
(
(
Q3
=V3
=
(
(
Q4
=V4
=
(
(
Q5
=V5
=
(
(
Q6
=V6
=
(
(
Q7
=V7
=
(
(
L1
=V8
=
1.000 F2
=
1.046*F2
.078
13.485@
(
.085)
( 12.369@
+ 1.000 E8
L2
=V9
L3
=V10 =
+ 1.000 E10
L4
=V11 =
+ 1.000 E11
L5
=V12 =
+ 1.000 E12
1.075*F2
.046
23.376@
(
.056)
( 19.108@
1.052*F2
.041
25.767@
(
.049)
( 21.370@
1.059*F2
.060
17.619@
(
.066)
( 16.109@
+ 1.000 E9
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
F2
=F2
=
(
(
1.092*F1
.143
7.639@
.126)
8.654@
+ 1.000 D2
USA sample (cnt.)
STANDARDIZED SOLUTION:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
L1
L2
L3
L4
L5
F2
=V1
=V2
=V3
=V4
=V5
=V6
=V7
=V8
=V9
=V10
=V11
=V12
=F2
=
=
=
=
=
=
=
=
=
=
=
=
=
.715 F1
.691*F1
.851*F1
.878*F1
.873*F1
.876*F1
.830*F1
.963 F2
.821*F2
.951*F2
.966*F2
.895*F2
.781*F1
R-SQUARED
+
+
+
+
+
+
+
+
+
+
+
+
+
.699
.723
.525
.478
.489
.482
.557
.269
.571
.309
.258
.446
.625
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
D2
.511
.477
.725
.771
.761
.768
.689
.927
.674
.905
.934
.801
.609
Multiple group
España - USA
/TITLE
Model built by EQS 6 for Windows in Group 1
/SPECIFICATIONS
DATA='c:\eqs61\espa_auto.ess';
VARIABLES=12; CASES=162; GROUPS=2;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 =
*F2 + E10;
V11 =
*F2 + E11;
V12 =
*F2 + E12;
F2 =
*F1 + D2;
/VARIANCES
F1 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E10 = *;
E11 = *;
E12 = *;
D2 = *;
/COVARIANCES
/END
/TITLE
Model built by EQS 6 for Windows in Group 2
/SPECIFICATIONS
DATA='C:\EQS61\usa_auto.ESS';
VARIABLES=12; CASES=109;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 =
*F2 + E10;
V11 =
*F2 + E11;
V12 =
*F2 + E12;
F2 =
*F1 + D2;
/VARIANCES
F1 = *;
E1 TO E12 = *;
D2 = *;
/COVARIANCES
/PRINT
FIT=ALL;
TABLE=EQUATION;
/LMTEST
PROCESS=SIMULTANEOUS;
SET=PVV,PFV,PFF,PDD,GVV,GVF,GFV,GFF,
BVF,BFF;
/END
España - USA
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE
INDEPENDENCE AIC =
MODEL AIC =
2925.47346
20.59547
=
3189.473 ON
INDEPENDENCE CAIC =
MODEL CAIC =
132 DEGREES OF FREEDOM
2320.45195
-465.25514
CHI-SQUARE =
232.595 BASED ON
106 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.927
BENTLER-BONETT NON-NORMED FIT INDEX =
.948
COMPARATIVE FIT INDEX (CFI)
=
.959
BOLLEN
(IFI) FIT INDEX
=
.959
MCDONALD (MFI) FIT INDEX
=
.788
LISREL
GFI FIT INDEX
=
.882
LISREL
AGFI FIT INDEX
=
.826
ROOT MEAN-SQUARE RESIDUAL (RMR)
=
.109
STANDARDIZED RMR
=
.039
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.055,
=
.067
.079)
España – USA
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
1597.63751
-52.85913
1861.638 ON
INDEPENDENCE CAIC =
MODEL CAIC =
SATORRA-BENTLER SCALED CHI-SQUARE =
159.1409 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
132 DEGREES OF FREEDOM
992.61600
-538.70974
106 DEGREES OF FREEDOM
.00065
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
1170.047
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
216.729
.00000
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
106,
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.915
BENTLER-BONETT NON-NORMED FIT INDEX =
.962
COMPARATIVE FIT INDEX (CFI)
=
.969
BOLLEN
(IFI) FIT INDEX
=
.970
MCDONALD (MFI) FIT INDEX
=
.905
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.029,
6.665
160
.00000
=
.044
.057)
Multiple group
Equality restrictions
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
España - USA
/TITLE
Model built by EQS 6 for Windows in Group 1
/SPECIFICATIONS
DATA='c:\eqs61\espa_auto.ess';
VARIABLES=12; CASES=162; GROUPS=2;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 = 1F1 + E1;
V2 = *F1 + E2;
V3 = *F1 + E3;
V4 = *F1 + E4;
V5 = *F1 + E5;
V6 = *F1 + E6;
V7 = *F1 + E7;
V8 = 1F2 + E8;
V9 = *F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F2 = *F1 + D2;
/VARIANCES
F1 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E10 = *;
E11 = *;
E12 = *;
D2 = *;
/COVARIANCES
/END
/TITLE
Model built by EQS 6 for Windows in Group 2
/SPECIFICATIONS
DATA='C:\EQS61\usa_auto.ESS';
VARIABLES=12; CASES=109;
METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 =
*F2 + E10;
V11 =
*F2 + E11;
V12 =
*F2 + E12;
F2 =
*F1 + D2;
/VARIANCES
F1 = *;
E1 TO E12 = *;
D2 = *;
/COVARIANCES
/PRINT
FIT=ALL;
TABLE=EQUATION;
/LMTEST
PROCESS=SIMULTANEOUS;
SET=PVV,PFV,PFF,PDD,GVV,GVF,GFV,GFF,
BVF,BFF;
/CONSTRAINTS
(1,F2,F1)=(2,F2,F1);
/END
España - USA
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE
INDEPENDENCE AIC =
MODEL AIC =
2925.47346
18.67890
=
3189.473 ON
INDEPENDENCE CAIC =
MODEL CAIC =
132 DEGREES OF FREEDOM
2320.45195
-471.75521
CHI-SQUARE =
232.679 BASED ON
107 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.927
BENTLER-BONETT NON-NORMED FIT INDEX =
.949
COMPARATIVE FIT INDEX (CFI)
=
.959
BOLLEN
(IFI) FIT INDEX
=
.959
MCDONALD (MFI) FIT INDEX
=
.790
LISREL
GFI FIT INDEX
=
.882
LISREL
AGFI FIT INDEX
=
.828
ROOT MEAN-SQUARE RESIDUAL (RMR)
=
.110
STANDARDIZED RMR
=
.039
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.055,
=
.067
.078)
España - USA
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
1597.63751
-54.35661
1861.638 ON
INDEPENDENCE CAIC =
MODEL CAIC =
SATORRA-BENTLER SCALED CHI-SQUARE =
159.6434 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
132 DEGREES OF FREEDOM
992.61600
-544.79071
107 DEGREES OF FREEDOM
.00074
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
1180.522
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
217.085
.00000
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
107,
FIT INDICES
----------BENTLER-BONETT
NORMED FIT INDEX =
.914
BENTLER-BONETT NON-NORMED FIT INDEX =
.962
COMPARATIVE FIT INDEX (CFI)
=
.970
BOLLEN
(IFI) FIT INDEX
=
.970
MCDONALD (MFI) FIT INDEX
=
.906
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
90% CONFIDENCE INTERVAL OF RMSEA (
.028,
6.620
159
.00000
=
.043
.056)
Spain - USA
Equality among
groups
Unrestricted model:
- chi-square =
- df= 106
232.595
Restricted model (nested):
- chi-square =
232.67
- df= 107
Difference testing (Δ χ2): (Ho = Equality among groups)
-chi-cuadrado (dif.) = 0.08 (232.67 – 232.59)
-Grados de libertad (dif.) = 1 (107 – 106)
-P-value ≈ 1
The Δ χ2 is not statistically significant, so we accept the model of equality of
of parameters across groups
Means and covariances
(MACS)
Model with the means
Q1
Q2
L1
Q3
L2
Q4
Calidad
Lealtad
L3
Q5
L4
Q6
L5
Q7
1
Spanish sample
/TITLE
modelo_espana
/SPECIFICATIONS
DATA='E:\raw_data\espa_auto.ess';
VARIABLES=12; CASES=162;
METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
*V999 + 1F1 + E1;
V2 =
*V999 + *F1 + E2;
V3 =
*V999 + *F1 + E3;
V4 =
*V999 + *F1 + E4;
V5 =
*V999 + *F1 + E5;
V6 =
*V999 + *F1 + E6;
V7 =
*V999 + *F1 + E7;
V8 =
*V999 + 1F2 + E8;
V9 =
*V999 + *F2 + E9;
V10 = *V999 + *F2 + E10;
V11 = *V999 + *F2 + E11;
V12 = *V999 + *F2 + E12;
F2 =
*F1 + D2;
/VARIANCES
F1 = *;
E1 TO E12 = *;
D2 = *;
/COVARIANCES
/lmtest
/PRINT
EIS;
FIT=ALL;
TABLE=EQUATION;
/END
Spanish sample (with means)
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
972.11041
-14.70280
1104.110 ON
INDEPENDENCE CAIC =
MODEL CAIC =
66 DEGREES OF FREEDOM
703.14894
-230.68701
SATORRA-BENTLER SCALED CHI-SQUARE =
91.2972 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
53 DEGREES OF FREEDOM
.00085
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
121.970
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
69.210
.06668
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
1.549
53,
107
.02863
FIT INDICES (BASED ON COVARIANCE MATRIX ONLY, NOT THE MEANS)
----------BENTLER-BONETT
NORMED FIT INDEX =
.917
BENTLER-BONETT NON-NORMED FIT INDEX =
.954
COMPARATIVE FIT INDEX (CFI)
=
.963
BOLLEN
(IFI) FIT INDEX
=
.964
MCDONALD (MFI) FIT INDEX
=
.887
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
=
.067
90% CONFIDENCE INTERVAL OF RMSEA (
.043,
.090)
The same fit than without me
Spanish sample (with means)
MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
Q1
=V1
=
4.881*V999
.130
37.570@
(
.130)
( 37.570@
+ 1.000 F1
+ 1.000 E1
Q2
=V2
=
4.837*V999 + 1.220*F1
.130
.125
37.189@
9.761@
(
.130)
(
.127)
( 37.189@
( 9.644@
+ 1.000 E2
Means of the Vs
Q3
=V3
=
5.106*V999 + 1.197*F1
.124
.120
41.154@
10.011@
(
.124)
(
.135)
( 41.154@
( 8.856@
+ 1.000 E3
Q4
=V4
=
5.244*V999 + 1.295*F1
.129
.125
40.805@
10.402@
(
.129)
(
.139)
( 40.805@
( 9.346@
+ 1.000 E4
Spanish sample (with means)
STANDARDIZED SOLUTION:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
L1
L2
L3
L4
L5
F2
=V1
=V2
=V3
=V4
=V5
=V6
=V7
=V8
=V9
=V10
=V11
=V12
=F2
=
=
=
=
=
=
=
=
=
=
=
=
=
.000*V999
.000*V999
.000*V999
.000*V999
.000*V999
.000*V999
.000*V999
.928 F2
.650*F2
.907*F2
.918*F2
.852*F2
.829*F1
R-SQUARED
+
+
+
+
+
+
+
+
+
+
+
+
+
.686 F1
.836*F1
.860*F1
.898*F1
.770*F1
.777*F1
.777*F1
.000*V999
.000*V999
.000*V999
.000*V999
.000*V999
.559 D2
+
+
+
+
+
+
+
+
+
+
+
+
.728
.549
.511
.440
.637
.630
.629
.372
.760
.420
.396
.523
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
En la solución estandarizada, los intercepts son = 0 !!
.470
.699
.739
.807
.594
.604
.604
.862
.423
.823
.843
.726
.687
Spanish sample: equality of means
/TITLE
modelo_espana
/SPECIFICATIONS
DATA='E:\raw_data\espa_auto.ess';
VARIABLES=12; CASES=162;
METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
V1 =
*V999 + 1F1 + E1;
V2 =
*V999 + *F1 + E2;
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
1181.423 ON
72 DEGREES OF FREEDOM
V3 =
*V999 + *F1 + E3;
V4 =
*V999 + *F1 + E4;
INDEPENDENCE MODEL HAS BEEN MODIFIED TO INCLUDE 6
V5 =
*V999 + *F1 + E5;
CONSTRAINTS FROM THE SPECIFIED MODEL.
V6 =
*V999 + *F1 + E6;
V7 =
*V999 + *F1 + E7;
INDEPENDENCE AIC = 1037.42264
INDEPENDENCE CAIC =
744.01013
V8 =
*V999 + 1F2 + E8;
MODEL AIC =
35.41420
MODEL CAIC = -205.02106
V9 =
*V999 + *F2 + E9;
V10 = *V999 + *F2 + E10;
SATORRA-BENTLER SCALED CHI-SQUARE =
153.4142 ON
59 DEGREES OF FREEDOM
V11 = *V999 + *F2 + E11;
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
V12 = *V999 + *F2 + E12;
F2 =
*F1 + D2;
RESIDUAL-BASED TEST STATISTIC
=
247.067
/VARIANCES
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00000
F1 = *;
E1 TO E12 = *;
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
=
97.111
D2 = *;
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
.00131
/COVARIANCES
/CONSTRAINTS
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
=
2.660
(V1,V999) = (V2,V999);
DEGREES OF FREEDOM =
59,
101
(V1,V999) = (V3,V999);
PROBABILITY VALUE FOR THE F-STATISTIC IS
.00001
(V1,V999) = (V4,V999);
(V1,V999) = (V5,V999);
FIT INDICES (BASED ON MODIFIED INDEPENDENCE MODEL, AND
(V1,V999) = (V6,V999);
----------- BASED ON COVARIANCE MATRIX ONLY, NOT THE MEANS)
(V1,V999) = (V7,V999);
BENTLER-BONETT
NORMED FIT INDEX =
.913
/lmtest
BENTLER-BONETT NON-NORMED FIT INDEX =
.939
/PRINT
COMPARATIVE FIT INDEX (CFI)
=
.955
EIS;
BOLLEN
(IFI) FIT INDEX
=
.956
FIT=ALL;
MCDONALD (MFI) FIT INDEX
=
.856
TABLE=EQUATION;
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
=
.100
/END
90% CONFIDENCE INTERVAL OF RMSEA (
.081,
.119)
Spanish sample: mean on factors
Q1
Q2
L1
Q3
L2
Q4
Calidad
Lealtad
Q5
Q6
L3
L4
a
mx
Q7
1
L5
Spanish sample: mean on factors
/TITLE
modelo_espana
/SPECIFICATIONS
DATA='E:\raw_data\espa_auto.ess';
VARIABLES=12; CASES=162;
METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F1 = *V999 + D1;
F2 = *V999 + *F1 + D2;
/VARIANCES
! F1 = *; !COMANDO ELIMINADO
E1 TO E12 = *;
D1 TO D2 = *; !F1 “VARIABLE DEPENDIENTE”
/COVARIANCES
/CONSTRAINTS
/lmtest
/PRINT
EFFECT = YES;
EIS;
FIT=ALL;
TABLE=EQUATION;
/END
Spanish sample: mean on factors
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
1013.34309
-10.10755
1169.343 ON
INDEPENDENCE CAIC =
MODEL CAIC =
78 DEGREES OF FREEDOM
695.47954
-266.84350
SATORRA-BENTLER SCALED CHI-SQUARE =
115.8925 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
63 DEGREES OF FREEDOM
.00006
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
164.681
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
81.153
.06156
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
63,
1.595
97
.01904
FIT INDICES (BASED ON COVARIANCE MATRIX ONLY, NOT THE MEANS)
----------BENTLER-BONETT
NORMED FIT INDEX =
.902
BENTLER-BONETT NON-NORMED FIT INDEX =
.917
COMPARATIVE FIT INDEX (CFI)
=
.944
BOLLEN
(IFI) FIT INDEX
=
.945
MCDONALD (MFI) FIT INDEX
=
.825
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
=
.073
90% CONFIDENCE INTERVAL OF RMSEA (
.051,
.093)
The difference of d.f. …
Spanish sample: mean on factors
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
Mean of F1
F1
F2
=F1
=F2
=
=
4.852*V999
.135
35.968@
(
.137)
( 35.543@
+ 1.000 D1
1.085*F1
.073
14.879@
(
.062)
( 17.459@
-
Intercept
(
(
.061*V999
.349
-.176
.322)
-.190)
+ 1.000 D2
Spanish sample: mean on factors
DECOMPOSITION OF EFFECTS WITH NONSTANDARDIZED VALUES
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
PARAMETER TOTAL EFFECTS
----------------------F1
=F1
=
4.852*V999
+ 1.000 D1
Mean of F2
F2
D2
=F2
=
1.085*F1
.073
14.879@
(
.062)
( 17.459@
+ 5.203*V999
.138
37.787@
(
.652)
( 7.978@
+ 1.085 D1
.073
14.879@
(
.062)
( 17.459@
+ 1.000
Spanish sample: mean on factors
STANDARDIZED SOLUTION:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
L1
L2
L3
L4
L5
F1
F2
=V1
=V2
=V3
=V4
=V5
=V6
=V7
=V8
=V9
=V10
=V11
=V12
=F1
=F2
=
=
=
=
=
=
=
=
=
=
=
=
=
=
.722 F1
.804*F1
.853*F1
.877*F1
.817*F1
.801*F1
.766*F1
.937 F2
.657*F2
.904*F2
.915*F2
.821*F2
.000*V999
.827*F1
R-SQUARED
+ .692 E1
+ .595 E2
+ .522 E3
+ .481 E4
+ .576 E5
+ .598 E6
+ .643 E7
+ .349 E8
+ .754 E9
+ .428 E10
+ .402 E11
+ .571 E12
+1.000 D1
+ .000*V999
+ .562 D2
¡ The intercepts are 0 in the standardized solution !
.521
.646
.728
.769
.668
.642
.587
.878
.431
.817
.838
.674
.000
.684
Multi-group mean and
covariance structures
MG-MACS
Multi-group MACS
Q1
Q2
L1
Q3
L2
=
Q4
Calidad
Lealtad
Q5
Q6
Q7
L3
L4
a
=
Mx
=
1
Iguales entre grupos
L5
Multi-group MACS
/TITLE
Model built by EQS 6 for Windows in Group 1
/SPECIFICATIONS
DATA='E:\Raw_data\espa_auto.ess';
VARIABLES=12; CASES=162; GROUPS=2;
METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F1 = *V999 + D1;
F2 = *V999 + *F1 + D2;
/VARIANCES
! F1 = *; !COMANDO ELIMINADO
E1 TO E12 = *;
D1 TO D2 = *; !F1 VARIABLE DEPENDIENTE
/COVARIANCES
/END
Across-group constraints
/TITLE
Model built by EQS 6 for Windows in Group 2
/SPECIFICATIONS
DATA='E:\Raw_data\usa_auto.ESS';
VARIABLES=12; CASES=109;
METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW;
/LABELS
V1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5;
V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3;
V11=L4; V12=L5;
/EQUATIONS
V1 =
1F1 + E1;
V2 =
*F1 + E2;
V3 =
*F1 + E3;
V4 =
*F1 + E4;
V5 =
*F1 + E5;
V6 =
*F1 + E6;
V7 =
*F1 + E7;
V8 =
1F2 + E8;
V9 =
*F2 + E9;
V10 = *F2 + E10;
V11 = *F2 + E11;
V12 = *F2 + E12;
F1 = *V999 + D1;
F2 = *V999 + *F1 + D2;
/VARIANCES
! F1 = *; !COMANDO ELIMINADO
E1 TO E12 = *;
D1 TO D2 = *; !F1 VARIABLE DEPENDIENTE
/COVARIANCES
/PRINT
FIT=ALL;
TABLE=EQUATION;
/LMTEST
PROCESS=SIMULTANEOUS;
SET=PVV,PFV,PFF,PDD,GVV,GVF,GFV,GFF,
BVF,BFF;
/CONSTRAINTS
(1,F2,F1)=(2,F2,F1); !same slope across groups
(1,F1,V999) = (2,F1,V999); !same mean across groups
(1,F2,V999) = (2,F2,V999); !same intercept across groups
/END
Multisample MACS
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE =
INDEPENDENCE AIC =
MODEL AIC =
1677.03301
-44.65610
1989.033 ON
INDEPENDENCE CAIC =
MODEL CAIC =
SATORRA-BENTLER SCALED CHI-SQUARE =
213.3439 ON
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
156 DEGREES OF FREEDOM
962.00758
-635.92713
129 DEGREES OF FREEDOM
.00000
RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
= 38916.805
.00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS
=
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC
DEGREES OF FREEDOM =
PROBABILITY VALUE FOR THE F-STATISTIC IS
=
264.194
.00000
155.963
129,
137
.00000
FIT INDICES (BASED ON COVARIANCE MATRIX ONLY, NOT THE MEANS)
----------BENTLER-BONETT
NORMED FIT INDEX =
.896
BENTLER-BONETT NON-NORMED FIT INDEX =
.920
COMPARATIVE FIT INDEX (CFI)
=
.945
BOLLEN
(IFI) FIT INDEX
=
.947
MCDONALD (MFI) FIT INDEX
=
.828
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)
=
.050
90% CONFIDENCE INTERVAL OF RMSEA (
.037,
.061)
Multisample MACS
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST
STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH
@.
(ROBUST STATISTICS IN PARENTHESES)
F1
F2
=F1
=F2
=
=
5.062*V999
.103
49.170@
(
.105)
( 48.402@
+ 1.000 D1
1.086*F1
.059
18.542@
(
.052)
( 21.069@
-
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST
STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED
WITH @.
(ROBUST STATISTICS IN PARENTHESES)
F1
=F1
=
(
(
(
(
.217*V999
.294
-.740
.271)
-.801)
+ 1.000 D2
F2
D2
=F2
=
5.062*V999
.103
49.170@
.105)
48.402@
+
1.086*F1
(
(
.059
18.542@
.052)
21.069@
¡¡¡Same means, intercepts and slopes across groups!!!
-
(
(
1.000 D1
.217*V999
.294
-.740
.271)
-.801)
+
1.000