EFFICIENT SCREENING OF VARIABLE SUBSETS IN MULTIVARIATE STATISTICAL MODELS

In applied statistical studies, it is common to collect data on a large pool of candidate variables from which a small subset will be selected for further analysis. The practice of variable selection often combines the use of substantive knowledge with subjective judgment and data-based selection procedures. The most popular of such procedures are stepwise methods. However, stepwise selection methods have two fundamental shortcomings: a) Most theoretical results from classical statistics require the assumption that the set of variables to be analyzed was chosen independently of the data. Therefore, when the variables are selected based on the data, the results from classical distribution theory almost never hold. b) Stepwise selection methods look at one variable at a time and tend to ignore the impact of combining particular sets of variables together. Thus, as each variable “importance” is often influenced by the set variables currently under analysis, stepwise methods may fail to identify the most adequate variable subsets. The problems created by a) and b) are now widely recognized and have been discussed by several authors. Miller (1984, 1990) and Derksen and Keselman (1992) give good reviews of the relevant literature in the context of Regression Analysis. In the context of Discriminant Analysis the problems created by a) are discussed, among others, by Murray (1977), McKay and Campbel (1982a), Snapinn and Knoke (1989) and Turlot (1990), and the problems created by b) are discussed by Hand (1981), McKay and Campbel (1982a, 1982b) an