Model Criticism
There is a temptation to become personally attached to a particular model. Statisticians call this ‘falling in love with your model’. It is as well to remember the following truths about models:
- All models are wrong.
- Some models are better than others.
- The correct model can never be known with certainty.
- The simpler the model, the better it is.
There are several ways that we can improve things if it turns out that our present model is inadequate:
- Transform the response variable.
- Transform one or more of the explanatory variables.
- Try fitting different explanatory variables if you have any.
- Use a different error structure.
- Use non-parametric smoothers instead of parametric functions.
- Use different weights for different y values.
All of these are investigated in the coming chapters. In essence, you need a set of tools to establish whether, and how, your model is inadequate. For example, the model might:
- predict some of the y values poorly;
- show non-constant variance;
- show non-normal errors;
- be strongly influenced by a small number of influential data points;
- show some sort of systematic pattern in the residuals;
- exhibit overdispersion.
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