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SIGMA WorkshopPart 3: Statistical Screening

Gönenç Yücel

SESDYN Research Group

Boğaziçi University, Istanbul

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A brief introduction• What is stat screening?• What is it good for?• What does it rely on?

• Altering uncertain (exogenous) model parameters• Relating the value of an outcome of interest to changes in

parameter values• Uses correlation coefficient to quantify the degree and direction of

relationship between a parameter and the value of the outcome at a certain time point

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Background literature• Ford, A., & Flynn, H. (2005). Statistical screening of system dynamics

models. System Dynamics Review, 21(4), 273–303.

• Taylor, T., Ford, D., & Ford, A. (2007). Model Analysis Using Statistical Screening: Extensions and Example Applications . 25th International Conference of the System Dynamics Society. Boston: System Dynamics Society.

• Taylor, T. R. B., David N. Ford, & Ford, A. (2010). Improving model understanding using statistical screening. System Dynamics Review, 26(1), 73–87.

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Key Concept: Correlation Coefficients

• A measure of the linear correlation (dependence) between two variables X and Y, giving a value between +1 and −1 inclusive, where • 1 is total positive correlation, • 0 is no correlation, and • −1 is total negative correlation.

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Demo Model• Bass diffusion model• See Business Dynamics by Sterman (2000) for specifications of the

model • Vensim version of the model is available in the Stat Screening folder

on your computers

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Our demo task

• Perform a Statistical Screening Analysis on the demo model (i.e. Bass diffusion model) to evaluate the relative influence of• Two of the exogenous variables (i.e. contact rate and adoption

fraction) and • The one exogenous initial condition (i.e. initial potential adopters).

• Using the adoption rate (sales) as the main outcome of interest (performance variable).

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ProcedureA. Perform statistical screening to calculate correlation coefficients and to

plot these over time

B. Select a time period for analysis

C. Identify high-leverage parameters. • High-leverage parameters are the parameters with the highest absolute correlation

coefficient values during the selected time

D. Create a list of high leverage parameters and their related model structures

E. Use additional structure-behavior analysis methods (e.g. verbal reasoning, scenario analysis, behavioral analysis) to explain how each parameter the structures they influence drive the behavior of the system.

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A. Calculating Correlation Coefficients

1. Select uncertain model input parameters and a single performance variable for analysis

2. Specify a distribution for each uncertain model parameter

3. Simulate the model using a combination of values from the specified distributions (e.g. Using Vensim’s Sensitivity Analysis feature)

4. Export the results of the simulation set

5. Pick up the Excel template that best fits the simulation set

6. Import the results from the simulation set to the Excel template, and observe the plot of the correlation coefficients

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Steps A.1 & A.2• Selected parameters, and distributions

• Model parameters to be analyzed

• Model output to be analyzed• Adoption rate

ParameterReference

ValueRange to be

TestedDistribution

Contact rate 0.5 [0.25, 0.75] Uniform

Adoption fraction

0.5 [0.25, 0.75] Uniform

Initial Adopters

10 [5, 10] Uniform

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A. Calculating Correlation Coefficients

1. Select uncertain model input parameters and a single performance variable for analysis

2. Specify a distribution for each uncertain model parameter

3. Simulate the model using a combination of values from the specified distributions (e.g. Using Vensim’s Sensitivity Analysis feature)

4. Export the results of the simulation set

5. Pick up the Excel template that best fits the simulation set

6. Import the results from the simulation set to the Excel template, and observe the plot of the correlation coefficients

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Conducting a set of simulations on Vensim

• Monte Carlo option in Vensim• Lets us to specify ranges for the parameters as well as their

distribution

• We will need to specify 2 things• An input control file (.vsc file)• An output savelist file (.lst file)

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Step A.3 Simulation with combinations of parameter values

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A. Calculating Correlation Coefficients

1. Select uncertain model input parameters and a single performance variable for analysis

2. Specify a distribution for each uncertain model parameter

3. Simulate the model using a combination of values from the specified distributions (e.g. Using Vensim’s Sensitivity Analysis feature)

4. Export the results of the simulation set

5. Pick up the Excel template that best fits the simulation set

6. Import the results from the simulation set to the Excel template, and observe the plot of the correlation coefficients

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A.4 Exporting the simulation results

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A. Calculating Correlation Coefficients

1. Select uncertain model input parameters and a single performance variable for analysis

2. Specify a distribution for each uncertain model parameter

3. Simulate the model using a combination of values from the specified distributions (e.g. Using Vensim’s Sensitivity Analysis feature)

4. Export the results of the simulation set

5. Pick up the Excel template that best fits the simulation set

6. Import the results from the simulation set to the Excel template, and observe the plot of the correlation coefficients

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A.5 Choosing an Excel template• Choosing the right template!

• Number of parameters• Number of simulations• Number of data points in a single run

• In our example, we have• 3 parameters• 200 simulations• 100 data points for each simulation• The right template would be StatScreenTemplate-

3inputs200runs100saveperiods.xls

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A. Calculating Correlation Coefficients

1. Select uncertain model input parameters and a single performance variable for analysis

2. Specify a distribution for each uncertain model parameter

3. Simulate the model using a combination of values from the specified distributions (e.g. Using Vensim’s Sensitivity Analysis feature)

4. Export the results of the simulation set

5. Pick up the Excel template that best fits the simulation set

6. Import the results from the simulation set to the Excel template, and observe the plot of the correlation coefficients

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A.6 Importing the simulations results to the Excel template

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Self-study Practice• Repeat the statistical screening on a modified version of

the simple Bass diffusion model

• Modification:• Add a quitting flow that flows from the adopters to the potential

adopters stock• The amount of the flow is defined as

• Adopters * Quitting Fraction

• Reference value of the quitting fraction is set to be 0.1

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