Example of EQS with ‘raw data’ Sintaxis generator Method = robust Multiple group Mean and...
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Transcript of Example of EQS with ‘raw data’ Sintaxis generator Method = robust Multiple group Mean and...
Example of EQS with ‘raw data’Sintaxis generatorMethod = robustMultiple 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 muestra española/TITLEmodelo_espana/SPECIFICATIONSDATA='c:\eqs61\espa_auto.ess';VARIABLES=12; CASES=162; METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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/PRINTEIS;FIT=ALL;TABLE=EQUATION;/END
Modelo muestra española
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE = 1732.230 ON 66 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1600.22971 INDEPENDENCE CAIC = 1331.26824 MODEL AIC = 12.42112 MODEL CAIC = -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 107.321.
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) = .088 90% CONFIDENCE INTERVAL OF RMSEA ( .067, .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 = 1104.110 ON 66 DEGREES OF FREEDOM
INDEPENDENCE AIC = 972.11041 INDEPENDENCE CAIC = 703.14894 MODEL AIC = -14.70039 MODEL CAIC = -230.68461
SATORRA-BENTLER SCALED CHI-SQUARE = 91.2996 ON 53 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00085
RESIDUAL-BASED TEST STATISTIC = 121.970 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 69.210 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .06669
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 1.549 DEGREES OF FREEDOM = 53, 107 PROBABILITY VALUE FOR THE F-STATISTIC IS .02863
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) = .067 90% CONFIDENCE INTERVAL OF RMSEA ( .043, .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 + 1.000 E2 .125 9.761@ ( .127) ( 9.644@
Q3 =V3 = 1.197*F1 + 1.000 E3 .120 10.011@ ( .135) ( 8.856@
Q4 =V4 = 1.295*F1 + 1.000 E4 .125 10.402@ ( .139) ( 9.346@
Q5 =V5 = 1.016*F1 + 1.000 E5 .112 9.062@ ( .135) ( 7.551@
Q6 =V6 = 1.103*F1 + 1.000 E6 .121 9.130@ ( .155) ( 7.101@
Q7 =V7 = 1.103*F1 + 1.000 E7 .121 9.136@ ( .130) ( 8.471@
L1 =V8 = 1.000 F2 + 1.000 E8 L2 =V9 = .786*F2 + 1.000 E9 .079 9.933@ ( .066) ( 11.854@
L3 =V10 = 1.051*F2 + 1.000 E10 .053 19.683@ ( .046) ( 22.782@
L4 =V11 = 1.078*F2 + 1.000 E11 .053 20.415@ ( .047) ( 22.967@
L5 =V12 = 1.056*F2 + 1.000 E12 .064 16.585@ ( .052) ( 20.327@
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 + 1.000 D2 .125 9.168@ ( .144) ( 7.943@
… spanish sample(cnt.)
STANDARDIZED SOLUTION: R-SQUARED
Q1 =V1 = .686 F1 + .728 E1 .470 Q2 =V2 = .836*F1 + .549 E2 .699 Q3 =V3 = .860*F1 + .511 E3 .739 Q4 =V4 = .898*F1 + .440 E4 .807 Q5 =V5 = .771*F1 + .637 E5 .594 Q6 =V6 = .777*F1 + .630 E6 .603 Q7 =V7 = .777*F1 + .629 E7 .604 L1 =V8 = .928 F2 + .372 E8 .862 L2 =V9 = .650*F2 + .760 E9 .423 L3 =V10 = .907*F2 + .420 E10 .823 L4 =V11 = .918*F2 + .396 E11 .843 L5 =V12 = .852*F2 + .523 E12 .726 F2 =F2 = .829*F1 + .559 D2 .688
USA sample/TITLEmodelo_USA/SPECIFICATIONSDATA='c:\eqs61\usa_auto.ess';VARIABLES=12; CASES=109; METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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/PRINTEIS;FIT=ALL;TABLE=EQUATION;/END
USA sample (cnt.) GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE = 1457.244 ON 66 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1325.24370 INDEPENDENCE CAIC = 1083.45672 MODEL AIC = 8.17449 MODEL CAIC = -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 105.399.
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) = .105 90% CONFIDENCE INTERVAL OF RMSEA ( .078, .130)
USA sample (cnt.) GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 784.463 ON 66 DEGREES OF FREEDOM
INDEPENDENCE AIC = 652.46267 INDEPENDENCE CAIC = 410.67569 MODEL AIC = -35.78090 MODEL CAIC = -229.94317
SATORRA-BENTLER SCALED CHI-SQUARE = 70.2191 ON 53 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .05675
RESIDUAL-BASED TEST STATISTIC = 150.778 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 62.242 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .18031
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 1.436 DEGREES OF FREEDOM = 53, 53 PROBABILITY VALUE FOR THE F-STATISTIC IS .09554
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) = .056 90% CONFIDENCE INTERVAL OF RMSEA ( .000, .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 + 1.000 E2 .129 6.940@ ( .118) ( 7.594@
Q3 =V3 = 1.072*F1 + 1.000 E3 .125 8.578@ ( .126) ( 8.518@
Q4 =V4 = 1.132*F1 + 1.000 E4 .128 8.853@ ( .117) ( 9.634@
Q5 =V5 = .999*F1 + 1.000 E5 .114 8.795@ ( .110) ( 9.052@
Q6 =V6 = 1.165*F1 + 1.000 E6 .132 8.832@ ( .124) ( 9.416@
Q7 =V7 = 1.218*F1 + 1.000 E7 .146 8.363@ ( .130) ( 9.349@
L1 =V8 = 1.000 F2 + 1.000 E8
L2 =V9 = 1.046*F2 + 1.000 E9 .078 13.485@ ( .085) ( 12.369@
L3 =V10 = 1.075*F2 + 1.000 E10 .046 23.376@ ( .056) ( 19.108@
L4 =V11 = 1.052*F2 + 1.000 E11 .041 25.767@ ( .049) ( 21.370@
L5 =V12 = 1.059*F2 + 1.000 E12 .060 17.619@ ( .066) ( 16.109@
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 + 1.000 D2 .143 7.639@ ( .126) ( 8.654@
USA sample (cnt.) STANDARDIZED SOLUTION: R-SQUARED
Q1 =V1 = .715 F1 + .699 E1 .511 Q2 =V2 = .691*F1 + .723 E2 .477 Q3 =V3 = .851*F1 + .525 E3 .725 Q4 =V4 = .878*F1 + .478 E4 .771 Q5 =V5 = .873*F1 + .489 E5 .761 Q6 =V6 = .876*F1 + .482 E6 .768 Q7 =V7 = .830*F1 + .557 E7 .689 L1 =V8 = .963 F2 + .269 E8 .927 L2 =V9 = .821*F2 + .571 E9 .674 L3 =V10 = .951*F2 + .309 E10 .905 L4 =V11 = .966*F2 + .258 E11 .934 L5 =V12 = .895*F2 + .446 E12 .801 F2 =F2 = .781*F1 + .625 D2 .609
España - USA/TITLEModel built by EQS 6 for Windows in Group 1/SPECIFICATIONSDATA='c:\eqs61\espa_auto.ess';
VARIABLES=12; CASES=162; GROUPS=2;METHOD=ML,ROBUST; ANALYSIS=COVARIANCE; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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
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 = 3189.473 ON 132 DEGREES OF FREEDOM
INDEPENDENCE AIC = 2925.47346 INDEPENDENCE CAIC = 2320.45195 MODEL AIC = 20.59547 MODEL CAIC = -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) = .067 90% CONFIDENCE INTERVAL OF RMSEA ( .055, .079)
España – USA GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1861.638 ON 132 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1597.63751 INDEPENDENCE CAIC = 992.61600 MODEL AIC = -52.85913 MODEL CAIC = -538.70974
SATORRA-BENTLER SCALED CHI-SQUARE = 159.1409 ON 106 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00065
RESIDUAL-BASED TEST STATISTIC = 1170.047 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 216.729 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 6.665 DEGREES OF FREEDOM = 106, 160 PROBABILITY VALUE FOR THE F-STATISTIC IS .00000
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) = .044 90% CONFIDENCE INTERVAL OF RMSEA ( .029, .057)
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
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 = 3189.473 ON 132 DEGREES OF FREEDOM
INDEPENDENCE AIC = 2925.47346 INDEPENDENCE CAIC = 2320.45195 MODEL AIC = 18.67890 MODEL CAIC = -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) = .067 90% CONFIDENCE INTERVAL OF RMSEA ( .055, .078)
España - USA GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1861.638 ON 132 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1597.63751 INDEPENDENCE CAIC = 992.61600 MODEL AIC = -54.35661 MODEL CAIC = -544.79071
SATORRA-BENTLER SCALED CHI-SQUARE = 159.6434 ON 107 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00074
RESIDUAL-BASED TEST STATISTIC = 1180.522 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 217.085 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 6.620 DEGREES OF FREEDOM = 107, 159 PROBABILITY VALUE FOR THE F-STATISTIC IS .00000
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) = .043 90% CONFIDENCE INTERVAL OF RMSEA ( .028, .056)
Spain - USA
Unrestricted model: - chi-square = 232.595 - df= 106
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
Equality among groups
Spanish sample/TITLEmodelo_espana/SPECIFICATIONSDATA='E:\raw_data\espa_auto.ess';VARIABLES=12; CASES=162; METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = *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/PRINTEIS;FIT=ALL;TABLE=EQUATION;/END
Spanish sample (with means) GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1104.110 ON 66 DEGREES OF FREEDOM
INDEPENDENCE AIC = 972.11041 INDEPENDENCE CAIC = 703.14894 MODEL AIC = -14.70280 MODEL CAIC = -230.68701
SATORRA-BENTLER SCALED CHI-SQUARE = 91.2972 ON 53 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00085
RESIDUAL-BASED TEST STATISTIC = 121.970 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 69.210 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .06668
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 1.549 DEGREES OF FREEDOM = 53, 107 PROBABILITY VALUE FOR THE F-STATISTIC IS .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 means!!!
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 + 1.000 F1 + 1.000 E1 .130 37.570@ ( .130) ( 37.570@
Q2 =V2 = 4.837*V999 + 1.220*F1 + 1.000 E2 .130 .125 37.189@ 9.761@ ( .130) ( .127) ( 37.189@ ( 9.644@
Q3 =V3 = 5.106*V999 + 1.197*F1 + 1.000 E3 .124 .120 41.154@ 10.011@ ( .124) ( .135) ( 41.154@ ( 8.856@
Q4 =V4 = 5.244*V999 + 1.295*F1 + 1.000 E4 .129 .125 40.805@ 10.402@ ( .129) ( .139) ( 40.805@ ( 9.346@
Means of the Vs
Spanish sample (with means)
STANDARDIZED SOLUTION: R-SQUARED
Q1 =V1 = .000*V999 + .686 F1 + .728 E1 .470 Q2 =V2 = .000*V999 + .836*F1 + .549 E2 .699 Q3 =V3 = .000*V999 + .860*F1 + .511 E3 .739 Q4 =V4 = .000*V999 + .898*F1 + .440 E4 .807 Q5 =V5 = .000*V999 + .770*F1 + .637 E5 .594 Q6 =V6 = .000*V999 + .777*F1 + .630 E6 .604 Q7 =V7 = .000*V999 + .777*F1 + .629 E7 .604 L1 =V8 = .928 F2 + .000*V999 + .372 E8 .862 L2 =V9 = .650*F2 + .000*V999 + .760 E9 .423 L3 =V10 = .907*F2 + .000*V999 + .420 E10 .823 L4 =V11 = .918*F2 + .000*V999 + .396 E11 .843 L5 =V12 = .852*F2 + .000*V999 + .523 E12 .726 F2 =F2 = .829*F1 + .559 D2 .687
En la solución estandarizada, los intercepts son = 0 !!
Spanish sample: equality of means /TITLEmodelo_espana/SPECIFICATIONSDATA='E:\raw_data\espa_auto.ess';VARIABLES=12; CASES=162; METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = *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/CONSTRAINTS(V1,V999) = (V2,V999);(V1,V999) = (V3,V999);(V1,V999) = (V4,V999);(V1,V999) = (V5,V999);(V1,V999) = (V6,V999);(V1,V999) = (V7,V999);/lmtest/PRINTEIS;FIT=ALL;TABLE=EQUATION;/END
GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1181.423 ON 72 DEGREES OF FREEDOM
INDEPENDENCE MODEL HAS BEEN MODIFIED TO INCLUDE 6 CONSTRAINTS FROM THE SPECIFIED MODEL.
INDEPENDENCE AIC = 1037.42264 INDEPENDENCE CAIC = 744.01013 MODEL AIC = 35.41420 MODEL CAIC = -205.02106
SATORRA-BENTLER SCALED CHI-SQUARE = 153.4142 ON 59 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
RESIDUAL-BASED TEST STATISTIC = 247.067 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 97.111 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00131
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 2.660 DEGREES OF FREEDOM = 59, 101 PROBABILITY VALUE FOR THE F-STATISTIC IS .00001
FIT INDICES (BASED ON MODIFIED INDEPENDENCE MODEL, AND ----------- BASED ON COVARIANCE MATRIX ONLY, NOT THE MEANS) BENTLER-BONETT NORMED FIT INDEX = .913 BENTLER-BONETT NON-NORMED FIT INDEX = .939 COMPARATIVE FIT INDEX (CFI) = .955 BOLLEN (IFI) FIT INDEX = .956 MCDONALD (MFI) FIT INDEX = .856 ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA) = .100 90% CONFIDENCE INTERVAL OF RMSEA ( .081, .119)
Spanish sample: mean on factors /TITLEmodelo_espana/SPECIFICATIONSDATA='E:\raw_data\espa_auto.ess';VARIABLES=12; CASES=162; METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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/PRINTEFFECT = YES;EIS;FIT=ALL;TABLE=EQUATION;/END
Spanish sample: mean on factors GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1169.343 ON 78 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1013.34309 INDEPENDENCE CAIC = 695.47954 MODEL AIC = -10.10755 MODEL CAIC = -266.84350
SATORRA-BENTLER SCALED CHI-SQUARE = 115.8925 ON 63 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00006
RESIDUAL-BASED TEST STATISTIC = 164.681 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 81.153 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .06156
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 1.595 DEGREES OF FREEDOM = 63, 97 PROBABILITY VALUE FOR THE F-STATISTIC IS .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)
F1 =F1 = 4.852*V999 + 1.000 D1 .135 35.968@ ( .137)
( 35.543@
F2 =F2 = 1.085*F1 - .061*V999 + 1.000 D2 .073 .349 14.879@ -.176 ( .062) ( .322)
( 17.459@ ( -.190)
Mean of F1
Intercept
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
F2 =F2 = 1.085*F1 + 5.203*V999 + 1.085 D1 + 1.000 D2
.073 .138 .073 14.879@ 37.787@ 14.879@ ( .062) ( .652) ( .062) ( 17.459@ ( 7.978@ ( 17.459@
Mean of F2
Spanish sample: mean on factors STANDARDIZED SOLUTION: R-SQUARED
Q1 =V1 = .722 F1 + .692 E1 .521 Q2 =V2 = .804*F1 + .595 E2 .646 Q3 =V3 = .853*F1 + .522 E3 .728 Q4 =V4 = .877*F1 + .481 E4 .769 Q5 =V5 = .817*F1 + .576 E5 .668 Q6 =V6 = .801*F1 + .598 E6 .642 Q7 =V7 = .766*F1 + .643 E7 .587 L1 =V8 = .937 F2 + .349 E8 .878 L2 =V9 = .657*F2 + .754 E9 .431 L3 =V10 = .904*F2 + .428 E10 .817 L4 =V11 = .915*F2 + .402 E11 .838 L5 =V12 = .821*F2 + .571 E12 .674 F1 =F1 = .000*V999 +1.000 D1 .000 F2 =F2 = .827*F1 + .000*V999 + .562 D2 .684
¡ The intercepts are 0 in the standardized solution !
Multi-group MACS
Calidad
Q2
Q3
Q4
Q5
Q7
Q1
Q6
Lealtad
L2
L3
L4
L5
L1
1
Mx=
a=
=
Iguales entre grupos
Multi-group MACS/TITLEModel built by EQS 6 for Windows in Group 1/SPECIFICATIONSDATA='E:\Raw_data\espa_auto.ess';VARIABLES=12; CASES=162; GROUPS=2;METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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
/TITLEModel built by EQS 6 for Windows in Group 2/SPECIFICATIONSDATA='E:\Raw_data\usa_auto.ESS';VARIABLES=12; CASES=109; METHOD=ML,ROBUST; ANALYSIS=MOMENTS; MATRIX=RAW; /LABELSV1=Q1; V2=Q2; V3=Q3; V4=Q4; V5=Q5; V6=Q6; V7=Q7; V8=L1; V9=L2; V10=L3; V11=L4; V12=L5; /EQUATIONSV1 = 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/PRINTFIT=ALL;TABLE=EQUATION;/LMTESTPROCESS=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
Across-group constraints
Multisample MACS GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST
ROBUST INDEPENDENCE MODEL CHI-SQUARE = 1989.033 ON 156 DEGREES OF FREEDOM
INDEPENDENCE AIC = 1677.03301 INDEPENDENCE CAIC = 962.00758 MODEL AIC = -44.65610 MODEL CAIC = -635.92713
SATORRA-BENTLER SCALED CHI-SQUARE = 213.3439 ON 129 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
RESIDUAL-BASED TEST STATISTIC = 38916.805 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED TEST STATISTIC = 264.194 PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
YUAN-BENTLER RESIDUAL-BASED F-STATISTIC = 155.963 DEGREES OF FREEDOM = 129, 137 PROBABILITY VALUE FOR THE F-STATISTIC IS .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 =F1 = 5.062*V999 + 1.000 D1 .103 49.170@ ( .105)
( 48.402@
F2 =F2 = 1.086*F1 - .217*V999 + 1.000 D2 .059 .294 18.542@ -.740 ( .052) ( .271)
( 21.069@ ( -.801)
CONSTRUCT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS
STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @.
(ROBUST STATISTICS IN PARENTHESES)
F1 =F1 = 5.062*V999 + 1.000 D1 .103 49.170@ ( .105)
( 48.402@
F2 =F2 = 1.086*F1 - .217*V999 + 1.000 D2
.059 .294 18.542@ -.740 ( .052) ( .271)
( 21.069@ ( -.801)
¡¡¡Same means, intercepts and slopes across groups!!!