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Example 22
Examining the Short List of Models
E Click on the Specification Search toolbar. This displays a short list of models.
In the figure below, the short list shows the best model for each number of parameters.
It shows the best 16-parameter model, the best 17-parameter model, and so on. Notice
that all criteria agree on the best model when the comparison is restricted to models
with a fixed number of parameters. The overall best model must be on this list, no
matter which criterion is employed.
Figure 22-4: The best model for each number of parameters
This table shows that the best 17-parameter model fits substantially better than the best
16-parameter model. Beyond 17 parameters, adding additional parameters yields
relatively small improvements in fit. In a cost-benefit analysis, stepping from 16
parameters to 17 parameters has a relatively large payoff, while going beyond 17
parameters has a relatively small payoff. This suggests adopting the best 17-parameter
model, using a heuristic point of diminishing returns argument. This approach to
determining the number of parameters is pursued further later in this example (see
“Viewing the Best-Fit Graph for C” on p. 338 and “Viewing the Scree Plot for C” on
p. 340).