The R Book

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.