In this section, we will calibrate a diffusion model of the conversion of US households to electricity to fit real data from the US Department of Commerce. The quantity of households (Total US Households) increases exponentially over time and this drives the increase in quantities of both Non Electric Households and Electric Households. Non Electric Households are making contacts with Electric Households, discovering electricity, and eventually being converted to Electric Households. Any new households (net household additions) that are built are added to both Non Electric Households and Electric Households according to the split determined by fraction electric. As the number of Non Electric Households dwindles to zero, the fraction electric becomes one and all the new households built are Electric Households.
Validation of a model rests in part on comparing model behavior to time series data collected in the "real world." When a model is structurally complete and simulates properly, calibration of the model can proceed. Calibration involves finding the values of model Constants that make the model generate behavior curves that best fit the real world data.
It is possible to manually alter model Constants to try and achieve a better fit between the real world data and simulation output. For a complex model with many Constants to optimize and many variables or datasets to fit, this is very time consuming. Using optimization, Vensim will automatically vary the Constants of your choice and look for the best fit between the simulation output and your real world data.
For example, we might not know (with any accuracy) what the growth fraction is for new households (household addition rate). We select this parameter (a Constant) for the Vensim optimizer to calibrate. The optimizer will automatically search through many values for this parameter to find the best fit of model data with the real world data.
|Ø||Open the model electric.mdl contained in the UserGuide\chap18\calibrat directory. A completed exercise is in the Complete directory for reference.|
|Ø||Sketch the model and enter the equations as shown below. The Time Bounds are INITIAL TIME = 1900, FINAL TIME = 1979, TIME STEP = 0.125, Save results every TIME STEP with units Year.|