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8 ModelModifications

Bagozzi (1980) reported a study of performance and job satisfaction on an industrial sales force. Job satisfaction was predicted by

achievement motivation and performance. The variable

Performance was predicted by Verbal IQ and Self-esteem.

(19)

9 ModelModifications

/TITLE

Model built by EQS 6 for Windows /SPECIFICATIONS

DATA='c:\eqs61\examples\bagozzi.ess';

VARIABLES=8; CASES=122;

METHOD=ML; ANALYSIS=COVARIANCE; MATRIX=COVARIANCE;

/LABELS

V1=PERFORM; V2=SATISFC1; V3=SATISFC2; V4=ACHMOTV1; V5=ACHMOTV2;

V6=SLFESTM1; V7=SLFESTM2; V8=VERBALIQ;

/EQUATIONS

V1 = *F3 + *V8 + E1;

V2 = 1F1 + E2;

V3 = *F1 + E3;

V4 = 1F2 + E4;

V5 = *F2 + E5;

V6 = 1F3 + E6;

V7 = *F3 + E7;

F1 = *F2 + *V1 + D1;

/VARIANCES V8 = *;

F2 = *;

F3 = *;

E1 = *;

E2 = *;

E3 = *;

E4 = *;

E5 = *;

E6 = *;

E7 = *;

D1 = *;

/COVARIANCES F3,F2 = *;

/PRINT EIS;

FIT=ALL;

TABLE=EQUATION;

/END

(20)

10 ModelModifications

GOODNESS OF FIT SUMMARY FOR METHOD = ML

INDEPENDENCE MODEL CHI-SQUARE = 256.499 ON 28 DEGREES OF FREEDOM INDEPENDENCE AIC = 200.499 INDEPENDENCE CAIC = 93.986

MODEL AIC = -3.984 MODEL CAIC = -68.652 CHI-SQUARE = 30.016 BASED ON 17 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .02623 THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 27.296.

FIT INDICES ---

BENTLER-BONETT NORMED FIT INDEX = .883 BENTLER-BONETT NON-NORMED FIT INDEX = .906 COMPARATIVE FIT INDEX (CFI) = .943 BOLLEN'S (IFI) FIT INDEX = .946 MCDONALD'S (MFI) FIT INDEX = .948 JORESKOG-SORBOM'S GFI FIT INDEX = .947 JORESKOG-SORBOM'S AGFI FIT INDEX = .887 ROOT MEAN-SQUARE RESIDUAL (RMR) = .694 STANDARDIZED RMR = .091

ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA) = .080 90% CONFIDENCE INTERVAL OF RMSEA ( .027, .125)

(21)

11 ModelModifications

CHI-SQUARE = 30.016 BASED ON 17 DEGREES OF FREEDOM PROBABILITY FOR THE CHI-SQUARE STATISTIC IS .02623 COMPARATIVE FIT INDEX (CFI) = .943

Based on the EQS output, all the parameter estimates are significant with a very high CFI. The model has a chi-square value of 30.016 with 17 degree freedom and a probability value of 0.03. It is less than the 0.05 significant level, thus the model fitting hypothesis will be rejected.

Is there any way to improve the model so that the hypothesis

will not be rejected?

(22)

12 ModelModifications

To improve a model, one should always use an apriori approach. That is, you add

parameters to a more restricted model or remove parameters from a less restricted

model based on prior knowledge of the model specifications or your expectation of a true model. Through the chi-square tests of

nested model, you achieve the purpose of

model modifications.

(23)

13 ModelModifications

/TITLE

/LABELS

/EQUATIONS

V1 = *F3 + *V8 + E1;

V2 = 1F1 + E2;

V3 = *F1 + E3;

V4 = 1F2 + E4;

V5 = *F2 + E5;

V6 = 1F3 + E6;

V7 = *F3 + E7;

F1 = *F2 + *V1 + D1;

/VARIANCES V8 = *;

F2 = *;

F3 = *;

E1 TO E7 = *;

D1 = *;

/COVARIANCES F3,F2 = *;

/LMTEST /END

(24)

14 ModelModifications

MULTIVARIATE LAGRANGE MULTIPLIER TEST BY SIMULTANEOUS PROCESS IN STAGE 1 PARAMETER SETS (SUBMATRICES) ACTIVE AT THIS STAGE ARE:

PVV PFV PFF PDD GVV GVF GFV GFF BVF BFF

CUMULATIVE MULTIVARIATE STATISTICS UNIVARIATE INCREMENT

--- --- HANCOCK'S SEQUENTIAL STEP PARAMETER CHI-SQUARE D.F. PROB. CHI-SQUARE PROB. D.F. PROB.

---- --- --- ---- --- --- --- ---- --- 1 F3,V8 5.584 1 .018 5.584 .018 17 .996 2 F2,V8 13.186 2 .001 7.602 .006 16 .960

There exists two parameters are greater interests to be

added to the model to achieve a better fit. These two

parameters are (F3,V8) and (F2,V8)

(25)

15 ModelModifications

LAGRANGE MULTIPLIER TEST (FOR ADDING PARAMETERS)

ORDERED UNIVARIATE TEST STATISTICS:

HANCOCK STANDAR- CHI- 17 DF PARAMETER DIZED NO CODE PARAMETER SQUARE PROB. PROB. CHANGE CHANGE -- --- --- --- --- --- --- ---

1 2 2 F3,V8 5.584 .018 .996 -1.470 -.247 2 2 11 V6,V8 5.423 .020 .996 -.104 -.013 3 2 11 V5,V8 5.183 .023 .997 -.108 -.014 4 2 2 F2,V8 4.397 .036 .999 -1.056 -.246 5 2 11 V3,V8 3.743 .053 1.000 .104 .010 6 2 12 V3,F3 2.251 .134 1.000 .334 .073 7 2 15 F1,V8 1.823 .177 1.000 .093 .009 8 2 11 V4,V8 1.101 .294 1.000 -.047 -.007 9 2 12 V2,F3 .804 .370 1.000 -.243 -.044

…

23 2 11 V7,V8 .006 .938 1.000 .003 .000 24 2 20 V7,F1 .002 .968 1.000 .003 .001 25 2 0 V2,F1 .000 1.000 1.000 .000 .000 26 2 0 V6,F3 .000 1.000 1.000 .000 .000 27 2 0 V4,F2 .000 1.000 1.000 .000 .000

(26)

16 ModelModifications

Two parameters were added to the model. They are the

correlation between factor Achievement Motivation and Verbal IQ

and the correlation between factor Self-esteem and Verbal IQ. As

shown in green circles.

(27)

17 ModelModifications

/TITLE

/LABELS

/EQUATIONS

V1 = *F3 + *V8 + E1;

V2 = 1F1 + E2;

V3 = *F1 + E3;

V4 = 1F2 + E4;

V5 = *F2 + E5;

V6 = 1F3 + E6;

V7 = *F3 + E7;

F1 = *F2 + *V1 + *V8 + D1;

/VARIANCES V8 = *;

F2 = *;

F3 = *;

…

E7 = *;

D1 = *;

/COVARIANCES V8,F2 = *;

V8,F3 = *;

F3,F2 = *;

/PRINT EIS;

FIT=ALL;

TABLE=EQUATION;

/END

(28)

18 ModelModifications

GOODNESS OF FIT SUMMARY FOR METHOD = ML

INDEPENDENCE MODEL CHI-SQUARE = 256.499 ON 28 DEGREES OF FREEDOM INDEPENDENCE AIC = 200.499 INDEPENDENCE CAIC = 93.986

MODEL AIC = -16.887 MODEL CAIC = -70.144 CHI-SQUARE = 11.113 BASED ON 14 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .67717 THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 11.487.

FIT INDICES ---

BENTLER-BONETT NORMED FIT INDEX = .957 BENTLER-BONETT NON-NORMED FIT INDEX = 1.025 COMPARATIVE FIT INDEX (CFI) = 1.000 BOLLEN'S (IFI) FIT INDEX = 1.012 MCDONALD'S (MFI) FIT INDEX = 1.012 JORESKOG-SORBOM'S GFI FIT INDEX = .977 JORESKOG-SORBOM'S AGFI FIT INDEX = .940 ROOT MEAN-SQUARE RESIDUAL (RMR) = .234 STANDARDIZED RMR = .030

(29)

19 ModelModifications

CHI-SQUARE = 11.113 BASED ON 14 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .67717 THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 11.487.

COMPARATIVE FIT INDEX (CFI) = 1.000

After adding two parameters suggested by LMTEST, the fit of the model improves drastically. The model has become from marginally fit to significantly fit.

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