Running the General SEM with AMOS
AMOS Files: ...\OUPSEM\General_SEM\BM1.amw
...\OUPSEM\General_SEM\BM2.amw
...\OUPSEM\General_SEM\BM3.amw
Data Files:
...\OUPSEM\General_SEM\Bollen_p334.xls
[Example] A panel model of political democracy and industrialization for developing
countries, (Bollen, 1989, p.324)
Model specification
1
2
1
x1
x2
x1
x2

3
1
1960
1
y2
2
y3
3
y4
4
y1
1
1960
x3
x3
y1
11
y2
y3
y4
21
2
21
y5
2
1965
y5
5
y6
6
y7
7
y8
8
y6
y7
y8
x1 – GNP per capita
x2 – Energy consumption
x3 - % labor force industry
y1 – Freedom of press
y2 – Freedom of political
opposition
y3 – Fairness of election
y4 – Effectiveness of
elected legislatives
y5 – y1 in 1965
y6 – y2 in 1965
y7 – y3 in 1965
y8 – y4 in 1965
Input data:
rowtype_
n
cov
cov
cov
cov
cov
cov
cov
cov
cov
cov
cov
varname_ y1
y1
y2
y3
y4
y5
y6
y7
y8
x1
x2
x3
y2
75
6.89
6.25
5.84
6.09
5.06
5.75
5.81
5.67
0.73
1.27
0.91
y3
y4
y5
y6
y7
y8
x1
x2
x3
75
75
75
75
75
75
75
75
75
75
15.58
5.84
9.51
5.6
9.39
7.54
7.76
0.62
1.49
1.17
10.76
6.69
4.94
4.73
7.01
5.64
0.79
1.55
1.04
11.22
5.7
7.44
7.49
8.01
1.15
2.24
1.84
6.83
4.98
5.82
5.34
1.08
2.06
1.58
11.38
6.75
8.25
0.85
1.81
1.57
10.8
7.59
0.94
2
1.63
10.53
1.1
2.23
1.69
0.54
0.99
0.82
2.28
1.81
1.98
General SEM for Bowen & Guo SEM
page 1
[Run 1]
The objective of this run is to find out whether the specified model is a good measurement model.
The measurement model is a congeneric CFA with associative relations among all factors.
1.95
1
y1
6.48
1.00
1
y2
4.84
1
y3
1.04
1.30
1
y4
e3
2.88
e4
2.40
4.48
1
y5
4.341.00
1.28
1.26 y6
y7
.77
1.31
1
e63.50
1
e7
2.93
1
y8
1
1.00
2.19
1.82
x1
x2
e8
.09
.45
Indust60
e5
4.34
Demo65
.65
e2
5.33
1.35
Demo60
e1
1
d1.10
d2
.47
1
x3
d3
BM1: CFA 1 of Bollen Mode(1989) p.324
Chi-square = 70.575 (41 df), p=.003
RMSEA=.099
GFI=.856, CFI=.955
Results show that the model does not fit data well. From here, Dr. Bollen made three important
decisions to improve the model: (1) he allowed measurement errors for the same indicator variable
at the two time points to be correlated – the rationale of doing this is the need to specify
autoregressive errors explicitly; (2) he allowed the path coefficient linking the endogenous factor
to an indicator variable to have same value at both time points (i.e., path of DEMO60 to y2 = path
of DEMO65 to y6, and so on); and (3) he allowed the following pair of indicator variables to have
a correlational error at both times: “freedom of group opposition” and “effectiveness of the
legislative body”, that is, correlational errors of y2 and y4, y6 and y8.
General SEM for Bowen & Guo SEM
page 2
Comment: these are very important and smart respecifications that combine both statistical
and substantive rationales. Discussion: you could adopt other method to respecify the model,
such as using MIs, correlating additional measurement errors, etc. But none of these is as
clever as those adopted by Dr. Bollen!
[Run2]
Results show that the model has an excellent fit to data.
1.87
1
y1
7.58
1.00
1
y2
4.84
1.19
Demo60
y3
1
y4
e3
1.44
3.22
e4
.58
2.18
2.32
4.59
1
y5
4.641.00
1.19
1.18
.83
1.25
.45
y6
y7
1
2.19
1.82
1
e7
e8
.09
x1
1
d1.11
d2
.47
1
x3
1.37
3.30
1
y8
x2
.36
e63.55
1
1.00
Indust60
.71
e5
4.97
Demo65
.65
e2
4.95
1
1.18
1.25
e1
d3
BM2: CFA 2 of Bollen Mode(1989) p.324 - Respedification
Chi-square = 38.767 (38 df), p=.435
RMSEA=.017
GFI=.921, CFI=.999
General SEM for Bowen & Guo SEM
page 3
[Run 3]
We now run the general SEM as a path analysis, that is, change the curve lines into one-arrow
causal lines, while keeping all measurement features the same as Run 2.
.58
.71
2.18
.36
1.44
e1
y1
y4
y3
y2
1.00
1
1
1
1.19
1.18
z1
Demo60
e6
1
1
1.25
3.88
1
1.47
1.19
Demo65
.87
1
1
y8
y7
y6
1.00
e8
e7
e5
y5
3.30
3.55
4.97
2.32
e4
e3
e2
1
3.22
4.95
7.58
1.87
1.37
1.18 1.25
z2
1
.17
.60
.45
Indust60
1.00
x1
1
.09
d1
2.19
x2
1
.11
d2
1.82
x3
1
.47
d3
BM3: Structural Regression Model (A Panel Model) Bollen (1989) p.324
Chi-square = 38.767 (38 df), p=.435
RMSEA=.017
GFI=.921, CFI=.999
General SEM for Bowen & Guo SEM
page 4
Findings and Interpretations
R-squares:
Estimate
Demo60
.198
Demo65
.964
x1
.837
x2
x3
y8
y7
y6
y5
y4
y3
y2
y1
.952
.759
.687
.643
.570
.666
.702
.575
.476
.722
Interpretation
19.8% of the variation in democracy in
1960 is explained by the level of
industrialization in 1960.
96.4% of the variation in democracy in
1965 is explained by both the level of
industrialization in 1960 and the level of
democracy in 1960.
83.7% of the variation in the observed
variable x1 is determined by the latent
variable. Very high. This suggests a good
measurement model. This is true for all
other indicator variables.
Relatively low.
Standardized coefficients:
The standardized path coefficient of INDUST60 on DEMO65 is estimated as .186, meaning that
every one-standard-deviation-unit increase in industrialization of 1960 increases 0.186 standarddeviation-unit of democracy in 1965.
Direct, indirect, and total effects:
Indirect effect of INDUST60 on DEMO65 via DEMO60
= (1.468)*(.866) = 1.271
S.E. (indirect effect) = .866 2.396 2  1.4682.0752  .3602
Critical Ratio (indirect effect) = 1.271/.3602 = 3.5286
Effect
Direct
Indirect via
mediator
Total
General SEM for Bowen & Guo SEM
.601 (32.1% of total)
S.E.
.228
Use * to
indicate
significance
at .05 level
*
1.271 (67.9% of total)
.3602
*
Estimated Path
Coefficient
(Unstandardized)
1.872
page 5