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SIGMA Workshop Part 3: Statistical Screening Gönenç Yücel SESDYN Research Group Boğaziçi University, Istanbul 1

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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 2

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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. 3

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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. 4

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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 5

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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). 7

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Procedure A. 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. 8

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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 9

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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 10 Parameter Reference Value Range to be Tested Distribution Contact rate0.5[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 11

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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) 12

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Step A.3 Simulation with combinations of parameter values 14

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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 18

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A.4 Exporting the simulation results 19

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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 22

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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 23

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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 24

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A.6 Importing the simulations results to the Excel template 25

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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 31

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