Abstract

A review of the literature indicates that linear models are frequently used in situations in which decisions are made on the basis of multiple codable inputs. These models are sometimes used normatively to aid the decision maker, as a contrast with the decision maker in the clinical vs statistical controversy, to represent the decision maker "paramorphically" and to "bootstrap" the decision maker by replacing him with his representation. Examination of the contexts in which linear models have been successfully employed indicates that the contexts have the following structural characteristics in common: each input variable has a conditionally monotone relationship with the output; there is error of measurement; and deviations from optimal weighting do not make much practical difference. These characteristics ensure the success of linear models, which are so appropriate in such contexts that random linear models may perform quite well. 4 examples involving the prediction of such codable output variables as GPA and psychiatric diagnosis are analyzed in detail. In all 4 examples, random linear models yield predictions that are superior to those of human judges