Model validity, testing and analysis

1
Model validity, testing and analysis
Yaman Barlas Bogaziçi University Industrial
Engineering Department 34342 Bebek Istanbul,
Turkey ybarlas_at_boun.edu.tr http//www.ie.boun.edu.
tr/barlas SESDYN Group http//www.ie.boun.edu.t
r/labs/sesdyn/
2
Conceptual and Philosophical Foundations

• Model Validity and Types of Models
• Statistical Forecasting models (black box)
• Descriptive Policy models (transparent)
• Philosophical Aspects
• - Philosophy of Science
• - Logical Empiricim and Absolute Truth
• - Conversational justification relative truth
  (purpose)
• - Statistical significance testing
• (Barlas and Carpenter 1990 and Barlas 1996)

3
Two aspects of model validity

• Structure Validity
• Primary importance
• Special place in System Dynamics
• Behavior Validity
• Role in system dynamics
• The special type of behavior validity in system
  dynamics
• Ex ante versus ex post prediction
• (Barlas 1996 and 1989)

4
Overall Nature and Selected Tests ofFormal Model
Validation
5
Logical Sequence of Formal Steps ofModel
Validation
6
Structure Validity

• (Simulation Verification)
• Direct Structure Tests
• Crucial, yet highly qualitative and informal
• Distributed through the entire modeling
  methodology
• Indirect Structure Tests (Structure-oriented
  behavior)
• Crucial and partly quantitative and formal
• Tool SiS software

7
Indirect Structure Testing Software SiS

• Based on automated dynamic pattern recognition
• Extreme condition pattern testing
• Also in parameter calibration and policy design
• (Kanar 1999 Kanar and Barlas 1999 Bog et al
  2004)

8
Indirect Structure Testing Software (SiS)
Basic Dynamic Patterns
9
Indirect Structure Testing Software (SiS)
List of dynamic behavior pattern classes
10
Software Implementation
General Picture of the Processes in Validity
Testing mode
General Picture of the Processes in Parameter
Calibration mode
11
Sample Model Used with SiS
12
Validity Testing with Default Parameters
Simulation Output (with default base parameters)
Likelihood Values of simulation behavior
correctly classified as the GR2DB pattern
13
Validity Testing by Setting Parameters
Fig1 Simulation Output (with base parameters)
Fig2 Simulation Output (with changed
parameters)
Likelihood Values of simulation behavior in Fig2
compared to the NEXGR pattern
14
Parameter Calibration with Specified Pattern
Simulation Output (with base parameters)
The ranges and number of values tried for each
parameter
15
Result of the Parameter Calibration 
Simulation Output as Desired (after automated
parameter calibration)

• Best parameter set is 41
• Best Likelihood Result 1.2119776136254248
• Best Parameter Set
• 1. advertising effectiveness 0.25
• 2. customer sales effectiveness 6.0
• 3. sales size 1.0

16
Parameter Calibration with Input Data
A view of the SiS interface during parameter
calibration
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Result of the Parameter Calibration 
Fig1 Simulation Output (with base parameters)
Fig2 Simulation Output (after parameter
calibration to match the input pattern)

• Best parameter set is 21
• Best Likelihood Result 3.7109428620957883
• Best Parameter Set
• 1. advertising effectiveness 5.0
• 2. customer sales effectiveness 0.0

18
Behavior Validity

• Two types of patterns
• Steady state
• Transient
• Major pattern components
• Trend, periods, amplitudes, ...

19
Behavior Validity Testing Software BTS II
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Behavior Validity Testing Software BTS II
21
BTS II ToolsTrend Regression
Model y(t) a b t a 1.4272937 b 0.9913937
22
BTS II ToolsMoments

• Moment Calculations
• Of Data Points 100
• 1st Moment (Mean) 1.4272937
• 2nd Moment (Variance) 2.7107011

23
BTS II ToolsAutocorrelation
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BTS II ToolsAutocorrelation Test
25
BTS II ToolsSpectral Density Function
dominant period1 20 Value 16.1181481405124 do
minant period2 8 Value 0.373946663988869
26
BTS II ToolsCross correlation
Max CrossCorrelation 0.7367365 at lag 0
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BTS II ToolsAmplitude Estimation
Model y(t) a b sin ( 2 p t / period c
) a 1.4272937 b 1.9958872 c
0.3500578 Amplitude Estimate 3.9917744
28
BTS II ToolsDiscrepancy Coefficient

• Of Data Points 100
• U 0.0363687
• U1 0.0231044
• U2 0.0054147
• U3 0.9714809

29
BTS II ToolsTrend in Amplitude
30
BTS II ToolsTrend in Amplitude
constant 7.4321903 phase angle 3.1273996 trend
of amplitude const of amplitude
10.1432480 slope of amplitude
12.562881
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Uses of BTS II and SiS in Model Analysis

• Analysis Understanding the dynamic properties of
  the model
• BTS II can assist in quantifying, measuring and
  assessing dynamic pattern components
• SiS can assist in deeper structural analysis
  (related to qualitative pattern modes)

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Uses of BTS II and SiS in Policy Design

• BTS II can assist in numerical performance
  improvement policies
• SiS can assist in more structural dynamic pattern
  improvement
• Parameter calibration can be extended to cover
  automated policy design

33
Implementation Issues

• More tools
• User friendliness
• More thorough (field) testing of the tools
• Better integration with simulation software
• ...

34
Policy Implementation Issues

• Validity of the policy recommendation
• (Robustness, timing, duration, transition...)
• Finally, validity of the implementation itself
• Validated model means just a reliable laboratory
  implementation validity does not automatically
  follow it is a whole area in itself

35
Concluding Observations

• Validity as a process, rather than an outcome
• Continuous (prolonged) validity testing
• Validation, analysis and policy design all
  integrated
• From validity towards quality
• Quality built-in versus inspected-in
• Group model building
• Testing by interactive gaming

36
Back to philosophy...

• A gradual, continuous, multi-method, qualitative
  and quantitative, formal and informal process of
  establishing confidence in a model. We should use
  any formal test/tool compatible with this
  philosophy, but never assume that tools
  themselves would be sufficient without proper
  philosophy

37
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