example of eqs with ‘raw data’

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

Calidad

Q2

Q3

Q4

Q5

Q7

Q1

Q6

Lealtad

L2

L3

L4

L5

L1

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




THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 105.399.


USA sample (cnt.) GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST








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

Multiple group

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

/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





España – USA GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST








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





España - USA GOODNESS OF FIT SUMMARY FOR METHOD = ROBUST








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

Means and covariances (MACS)

Model with the means

Calidad

Q2

Q3

Q4

Q5

Q7

Q1

Q6

Lealtad

L2

L3

L4

L5

L1

1

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







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


INDEPENDENCE MODEL HAS BEEN MODIFIED TO INCLUDE 6 CONSTRAINTS FROM THE SPECIFIED MODEL.






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

Calidad

Q2

Q3

Q4

Q5

Q7

Q1

Q6

Lealtad

L2

L3

L4

L5

L1

1

mx a

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








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 mean and covariance structures

MG-MACS

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








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!!!

example of eqs with ‘raw data’

Documents

fit indices

chisquare statistic

bollen ifi fit index

mcdonald mfi fit index

comparative fit index

lisrel gfi fit index

lisrel agfi fit index

independence caic