ABSTRACT
In this chapter we look at the problem of finding one or more subsets of variables whose models fit a set of data fairly well. Though we will only be looking at models that fit well in the least-squares sense, similar ideas can be applied with other measures of goodness-of-fit. For instance, there have been considerable developments in the fitting of models to categorical data, see e.g. Goodman (1971), Brown (1976), and Benedetti and Brown (1978), in which the measure of goodness-of-fit is either a log-likelihood or a chi-squared quantity. Other measures used in subset selection have included that of minimizing the maximum deviation from the model, known simply as minimax fitting or as L∞ fitting (e.g. Gentle and Kennedy (1978)), and fitting by maximizing the sum of absolute deviations or L1 fitting (e.g. Roodman (1974), Gentle and Hanson (1977), Narula and Wellington (1979), Wellington and Narula (1981)). Logistic regression is an important area of application of stepwise regression.
The model to be fitted in this case is
