2.2 Parameter Reduction: Further Notes
The concept of “parameter reduction” was already introduced in an earlier course: It refers to the idea that a model input (or parameter) which is of numerical form becomes replaced by a figure which is calculated from other inputs (thereby reducing the total number of independent inputs). These calculated “inputs” can be termed “quasi-inputs”, since they are formulas but are nevertheless essentially inputs. This allows for sensitivity analysis to be run more easily on models, for simpler forms of decisions to be analysed, and may allow for input values to be estimated more easily. Of course, such methods should only be used if doing so does not reduce the accuracy in a meaningful way or inhibit other uses of the model.
There is a range of cases for the complexity of the calculations involved in replacing the initial numerical fields with calculations. In the simplest case, the replaced values are simple cell references to a single cell containing an assumed value. An example is where the value of the growth rate is the same in each time period of the model, so that these growth rates can be replaced with a single figure (as done in the earlier model, shown again here for convenience):
In more complex cases, the replacement of the values may involve complex calculations or functions that involve several other inputs. An example is the interpolation that was used in the previous section:
Note that sometimes, the process of parameter reduction is not explicit; rather a model may be built directly in this form (such as when the model is built using a single growth rate that applies to all periods, or when the interpolation formula are built immediately into the model.
Such methods may also be combined. For example, in a long-term forecasting model, rather than having a separate growth rate in each period, one may:
- Short-term (e.g. years 1-2): Use a single input that serves as the growth rate for each of these years.
- Medium-term (e.g. years 3- 6): Use a tapered approach, to allow the growth to gradually adjust from the short-term assumption to the long-term rate.
- Long-term (e.g. from year 7 onwards). Use a single input that serves as the growth rate for each of these years.
In such cases, sensitivity analysis can then be conducted by varying the values of the reduced parameter set (i.e. the short-term growth, rate, the medium-term rate or the long-term rate).