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Example of EQS with ‘raw data’

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

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Example of EQS with ‘raw data’

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  1. Example of EQS with ‘raw data’ Sintaxis generator Method = robust Multiple group Mean and covariances (MACS)

  2. 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.

  3. Modelo Q1 Q2 L1 Q3 L2 Calidad Lealtad Q4 L3 Q5 L4 Q6 L5 Q7

  4. 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

  5. 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)

  6. 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

  7. 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)

  8. … 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@

  9. … 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

  10. 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

  11. 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)

  12. 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)

  13. USA sample (cnt.) 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@ 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@

  14. 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

  15. Multiple group

  16. España - USA /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 /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

  17. 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)

  18. 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)

  19. Multiple group Equality restrictions

  20. España - USA /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 • /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

  21. 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)

  22. 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)

  23. Spain - USA Equality among groups Unrestricted model: - chi-square = 232.595 - df= 106 Restricted model (nested): - chi-square = 232.67 - df= 107 • Difference testing (Δχ2): (Ho = Equality among groups) • chi-cuadrado (dif.) = 0.08 (232.67 – 232.59) • Grados de libertad (dif.) = 1 (107 – 106) • P-value ≈ 1 • The Δχ2is not statistically significant, so we accept the model of equality of • of parameters across groups

  24. Means and covariances (MACS)

  25. Model with the means Q1 Q2 L1 Q3 L2 Calidad Lealtad Q4 L3 Q5 L4 Q6 L5 Q7 1

  26. 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

  27. 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!!!

  28. 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

  29. 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 !!

  30. 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 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 /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 /PRINT EIS; 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)

  31. Spanish sample: mean on factors Q1 Q2 L1 Q3 L2 Calidad Lealtad Q4 L3 Q5 L4 Q6 L5 a mx Q7 1

  32. 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

  33. 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. …

  34. 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

  35. 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

  36. 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 !

  37. Multi-group mean and covariance structures MG-MACS

  38. Multi-group MACS Q1 Q2 L1 Q3 L2 = Calidad Lealtad Q4 L3 Q5 L4 Q6 L5 a = Mx = Q7 1 Iguales entre grupos

  39. /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 /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 Multi-group MACS Across-group constraints

  40. 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)

  41. 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) Multisample MACS ¡¡¡Same means, intercepts and slopes across groups!!!

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