Running a Non-Recursive Model with the General SEM
AMOS Files: ...\OUPSEM\General_SEM\BM1.amw
...\OUPSEM\General_SEM\BM2.amw
...\OUPSEM\General_SEM\BM3.amw
Data Files:
...\OUPSEM\General_SEM\Bagozzi1980.xls
Sources: Bagozzi, R.P. (1980), “Performance and satisfaction in an industrial sales force: An
examination of their antecedents and simultaneity”, Journal of Marketing, 44: 65-77.
Joreskog, K., & Sorbom, D. (1996), “LISREL 8: User’s Reference Guide”, Chicago, IL:
Scientific Software International, Inc.
Data: N=122 collected from an industrial sales force.
Research questions:
 Controlling for exogenous factors (i.e., achievement motivation, task-specific self esteem,
and verbal intelligence), is the relationship between performance and job satisfaction myth
or reality?
 Controlling for exogenous factors (i.e., achievement motivation, task-specific self esteem,
and verbal intelligence), does performance influence satisfaction, or does satisfaction
influence performance?
The general conceptual model can be expressed by the following path diagram:
z2
1
1
d1
1
d2
1
d3
d4
1
x1
x2
x3
x4
1
Achivement
Motiviation
1
Task-specific
Self Esteem
1
?
1
e2
e3
z1
1
1
1
1
?
Performance
x5
y2
y3
Job
Satisfaction
y1
Verbal
Intelligence
The input data:
Nonrecursive SEM for Bowen & Guo SEM
page 1
rowtype_
n
corr
corr
corr
corr
corr
corr
corr
corr
stddev
mean
varname_ y1
y1
y2
y3
x1
x2
x3
x4
x5
y2
y3
122
1
0.418
0.394
0.129
0.189
0.544
0.507
-0.357
2.09
720.86
x1
x2
x3
x4
x5
122
122
122
122
122
122
122
1
0.627
0.202
0.284
0.281
0.225
-0.156
3.43
15.54
1
0.266
0.208
0.324
0.314
-0.038
2.81
18.46
1
0.365
0.201
0.172
-0.199
1.95
14.9
1
0.161
0.174
-0.277
2.06
14.35
1
0.546
-0.294
2.16
19.57
1
-0.174
2.06
24.16
1
3.65
21.36
Notice that factors k3 (Verbal Intelligence) and n1 (Performance) are single-indicator latent
variables. To make the model identified, we impose a known variance for the measurement errors
x5 and y1, respectively. We assume a reliability of .85 for x5 and y1, then Var(d5)=1.998, and
Var(e1)=.655.
[Step 1, file “Job1.amw”]: To see whether or not we have a good measurement model.
Chi-square = 10.309 (12 df), p=.589
RMSEA=.000
GFI=.978, CFI=1.000
2.51
1
d1
2.54
1
d2
1.87
1
d3
2.10
1
d4
2.00
1
d5
1.67
.87
x1
Achivement
Motiviation
1.00
x2
1.15
x3
x4
1.00
Verbal
Intelligence
e3
.661
e1
1.00
y2
2.68
1
-1.87
11.22 -1.72 1.70
4.69
1
e2
.73
Task-specific
Self Esteem
1.00
x5
2.10
.86
6.98
1.89 .72
-1.10
Job
Satisfaction
y3
2.14
-2.70
3.68 2.80
y1
1.00
Performance
Job1: CFA Measurement model about
job satisfaction and performance (Bagozzi, 1980)
Nonrecursive SEM for Bowen & Guo SEM
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Comments:
 In general we have a good model, because all model-fit indices are excellent.
 All indicators have a loading greater than .8. Two R-squares are below .4, (i.e., R2 for
x1=.335, and R2 for x2=.398), indicating that these indicators are not highly determined by
their latent variables. Given that they are close to .4, we decided to keep them in the
analysis.
 No problematic MIs that indicate the need to correlate measurement errors.
 The estimated correlation between n1 (performance) and n2 (job satisfaction) is .553.
Given that the correlation is high and that the fundamental questions about the simultaneity
of performance and job satisfaction, we can form the following four rival hypothesis:
H1: the correlation is spurious; the two latent variables are correlated, because they are
both determined by common causes of k1, k2, and k3.
H2: n2 (job satisfaction) influences n1 (performance).
H3: n1 (performance) influences n2 (job satisfaction).
H4: n1 (performance) and n2 (job satisfaction) influence each other reciprocally.
[Step 2, file “Job2.amw”]: Test H1.
Chi-square = 10.309 (12 df), p=.589
RMSEA=.000
GFI=.978, CFI=1.000
4.29
z2
1
2.51
1
d1 2.54
1
d2
x11.00
x2
1.67
.87
Achivement
Motiviation
.88
1.00
Job
Satisfaction
.86 y2
y3
4.69
1
e2 2.68
1
1.05
e3
.73 .72
1.87
1
d3 2.10
1
d4
2.001
d5
x31.00
x4
x5
1.15
Task-specific
Self Esteem
1.00
-.12
2.10
.16-1.87
.97
-1.72
-.11
11.22
1.39
1
1.00
Performance
z1
y1
.66
1
e1
Verbal
Intelligence
Job 2: (Bagozzi, 1980) Test "H1: Spurious correlation of
job satisfaction & performance"
- They have the three exogenous factors as common causes
Nonrecursive SEM for Bowen & Guo SEM
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Results show that the estimated correlation between z1 and z2 is significant, p=.026. That means
that the three common causes cannot remove away all association between the two latent variables
(n1 and n2). Therefore, we should reject H1, and conclude that the correlation between n1 and n2
is not spurious.
We now go ahead to test H2. To do that, we need take out the correlation between z1 and z2,
because we want explicitly to test the causal relation between the two endogenous variables.
[Step 3, file “Job3.amw”]: Test H2.
Chi-square = 10.309 (12 df), p=.589
RMSEA=.000
GFI=.978, CFI=1.000
4.29
z2
1
2.51
1
d1 2.54
1
d2
x11.00
x2
1.67
.87
Achivement
Motiviation
.88
1.00
Job
Satisfaction
.86 y2
y3
4.69
1
e2 2.68
1
e3
.73 .72
1.87
1
d3 2.10
1
d4
2.001
d5
-.34
x31.00
x4
x5
1.15
Task-specific
Self Esteem
1.00
.25
2.10
.16-1.87
.79
-1.72
-.15
11.22
1.13
1
1.00
Performance
z1
y1
.66
1
e1
Verbal
Intelligence
Job 3: (Bagozzi, 1980) Test "H2: job satisfaction
influences performance"
Nonrecursive SEM for Bowen & Guo SEM
page 4
Results show that the structural path of n2 on n1 is significant, p=.017. We cannot reject H2.
[Step 4, file “Job4.amw”]: Test H3.
Chi-square = 10.309 (12 df), p=.589
RMSEA=.000
GFI=.978, CFI=1.000
3.49
z2
1
2.51
1
d1 2.54
1
d2
x11.00
x2
1.67
.87
Achivement
Motiviation
.97
1.00
Job
Satisfaction
.86 y2
y3
4.69
1
e2 2.68
1
e3
.73 -.01
1.87
1
d3 2.10
1
d4
2.001
d5
-.12
x31.00
x4
x5
1.15
Task-specific
Self Esteem
1.00
.76
2.10
.24-1.87
.97
-1.72
-.11
11.22
1.39
1
1.00
Performance
z1
y1
.66
1
e1
Verbal
Intelligence
Job 4: (Bagozzi, 1980) Test "H3 performance
influences job satisfaction"
Results show that the structural path of n1 on n2 is significant, p=.016. We cannot reject H3. The
two variables affect each other individually. Now it seems important to know whether or not a
reciprocal relation between the two variables exists.
Nonrecursive SEM for Bowen & Guo SEM
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[Step 5, file “Job5.amw”]: Test H4.
z2
1
1
d1
1
d2
1
d3
1
d4
x1
x2
x3
x4
1
Achivement
Motiviation
1
1
Task-specific
Self Esteem
1
1.998
1
x5
1
1
e2
1
e3
z1
1
Performance
d5
y2
y3
Job
Satisfaction
y1
0.655
1
e1
Verbal
Intelligence
Job 5: (Bagozzi, 1980) Test "H4: nonrecursive relation"
The model is underidentified. To solve the problem, we consider deleting the structural paths that
are not significant in Step 4. There are two of them: k1 on n1 (p=.564), and k2 on n2 (p=.975).
All other structural paths are significant.
Nonrecursive SEM for Bowen & Guo SEM
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[Step 6, file “Job6.amw”]: Test H4, delete two structural paths that are not significant from Step 5.
Chi-square = 10.474 (13 df), p=.655
RMSEA=.000
GFI=.978, CFI=1.000
3.53
z2
1
2.53
1
d1 2.50
1
d2
x11.00
x2
1.71
.85
Achivement
Motiviation
.92
1.00
Job
Satisfaction
.86 y2
y3
4.73
1
e2 2.66
1
e3
.70
1.84
1
d3 2.11
1
d4
2.001
d5
x31.00
x4
x5
1.15
1.00
-.05
2.10
Task-specific
Self Esteem
.25-1.89
.99
-1.73
-.09
11.22
1.55
.80
1
1.00
Performance
z1
y1
.66
1
e1
Verbal
Intelligence
Job 6: (Bagozzi, 1980) Test "H4: nonrecursive relation",
Delete two nonsignificant paths to make
the model identified
Results show that the model is good, but two structural coefficients are not significant: n2 on n1
(p=.668), and k3 on n1 (p=.108).
Clearly, the study cannot confirm a reciprocal relation between job satisfaction and performance.
Results cannot support the nonrecursive model!
Deleting the above two nonsignificant paths, we come up with the final model.
Nonrecursive SEM for Bowen & Guo SEM
page 7
[Step 7, file “Job7.amw”]: The final model.
Chi-square = 13.508 (15 df), p=.563
RMSEA=.000
GFI=.971, CFI=1.000
3.54
z2
1
2.54
1
d1 2.50
1
d2
x11.00
x2
1.71
.85
Achivement
Motiviation
.94
1.00
Job
Satisfaction
.85 y2
y3
4.62
1
e2 2.73
1
e3
.72
1.91
1
d3 2.21
1
d4
x31.00
x4
1.16
2.00
Task-specific
Self Esteem
.22-1.90
1.08
-1.97
2.001
d5
x5
1.00
1.35
.73
1
1.00
Performance
z1
y1
.66
1
e1
11.22
Verbal
Intelligence
Job 7: (Bagozzi, 1980) Final Model:
Delete nonsignificant paths of JOB6
Recursive Model
In this final model, all structural path coefficients are statistically significant at .05 level.
Interpretations? What did we find?
Nonrecursive SEM for Bowen & Guo SEM
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