To Main Proceedings Document
Analyzing Dynamic Systems: A
Comparison of System Dynamics and
Structural Equation Modeling
Peter Hovmand
School of Social Work
Michigan State University
Ralph Levine
Department of Psychology and
Department of Resource Development
Michigan State University
¢ Background
¢ Approach
¢ Comparisons
¢ Conclusions
Overview
Background
System dynamics modeling (SDM)
Structural equation modeling (SEM)
¢ Similarity of features that are modeled
¢ ‘Tendency to see SDM and SEM as the same
¢ Demonstrating differences between SDM
and SEM
Do SDM and SEM generate
“equivalent” models?
6, 0,
System 5 Structural
Dynamics Pen suveereeseesl > Equation
Model (SDM) Cc Model (SEM)
Approach
Develop a system dynamics model.
Use the system dynamics model to generate
simulated observed data, which implies by definition
that the system dynamics model fits the observed
data.
Generate structural equation models that fit the
observed data.
Test structural equation model fit with observed data,
which is then a test of fitness with the system
dynamics model.
“Fixes That Fail”
Causal Loop Diagram
6)
&g &q
+4
\I Yo
Latent Model
System Dynamics Model Structural Equation Model
anh =ENs +N, nN, =B.N3 +O,
on Ns =Ba, + Boo, +2.
OE =7Ns +m +8, N; =BxN, +6;
ons
ot
=-1.1-1); +N, +3.
Measurement Model
System Dynamics Model Structural Equation Model
y, (t,) =, (t,) +€, y, =, +€,
y(t.) =, (t,) +, y, =N, +€,
y3(t,) =, (t,) +, yz =N, +&,
a(t.) =I, (t,) +E, Ya =N, +E,
y5(t,) =z (t,) +€, Ys =N, TE;
Yo(t,) =. (t,) +E, Ye =N, +E
y,(t,) =, (t,) +E, yz SN; TE,
ya(t,) =I, (t,) +E, Ya =z TEs
Yo(t,) =N3(t,) +E Yo =N3 TE,
SDM
—Ftal
— Eta 2
— Eta 3
10
1% of simulated values
40
30 «
20 w iil! ,
ii
tit
: tell ul
104 ..! Ny pti "W! axl
3 ig Hie iytltnat
sf, hee
o i ait
a = = = = 7
in) 2 4 6 3 10
Time
| Etal
Eta 2
"| Eta3
LISREL Model 1
nnn
y4
»~
| yo
>) i
y7
D |
HE
Model 1 Chi-Square
Chi-Square
100.000
90.000
80.000
70.000
60.000
50.000
40.000
30.000
20.000
10.000
0.000
0.0
Model 1 RMSEA
RMSEA
1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
10.0
LISREL Model 2
oOo y
—~ +
sais is
y
Model 2 Chi-Square
Chi-Square
59.000
49.000
39.000
29.000 +
19.000 +
9.000
-1.000
Model 2 RMSEA
RMSEA
0.900
0.700
0.500
0.300
0.100
-0.100®
8.0
9.0
Summary of results
Phase of loop Time interval Dominant loop(s) | Model 1 Model 2
dominance fit fit
Pl 0.0 to 0.6 L1 andL2 No Yes
Transition 0.6 - No Yes
P2 0.6 to 2.4 L1 No Yes
Transition 2.4 - Yes No™?
P38 2.4 to 3.7 12 Yes Yes
Transition 3.7 7 Yes Now?
P4 3.7t0 6.3 L1 Yes Yes
Transition 6.3 - Yes Yes
P5 6.3 to 10.0 L1 andL2 Yes! Yes
T
RMSEA increases up to about 0.045 and then decreases again.
? Fails to converge.
* Not admissible after 50 iterations.
Conclusions
e The structural equation model that
corresponded to the system dynamics model
did not fit the data during the initial shifts in
loop dominance.
¢ The structural equation model that did fit
the data did not correspond to the system
dynamics model.
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