The R Book

Types of Statistical Model

Fitting models to data is the central function of R. The process is essentially one of exploration; there are no fixed rules and no absolutes. The object is to determine a minimal adequate model (see Table 9.1) from the large set of potential models that might be used to describe the given set of data. In this book we discuss five types of model:

• the null model;
• the minimal adequate model;
• the current model;
• the maximal model; and
• the saturated model.

The stepwise progression from the saturated model (or the maximal model, whichever is appropriate) through a series of simplifications to the minimal adequate model is made on the basis of deletion tests. These are F-tests or chi-squared tests that assess the significance of the increase in deviance that results when a given term is removed from the current model.

Table 9.1. Statistical modelling involves the selection of a minimal adequate model from a potentially large set of more complex models, using stepwise model simplification.

Model	Interpretation
Saturated model	One parameter for every data point Fit: perfect Degrees of freedom: none Explanatory power of the model: none
Maximal model	Contains all (p) factors, interactions and covariates that might be of any interest. Many of the model's terms are likely to be insignificant Degrees of freedom: n − p − 1 Explanatory power of the model: it depends
Minimal adequate model	A simplified model with 0 ≤ p′ ≤ p parameters Fit: less than the maximal ...