Unit-weighted Regression - Literature Review

Literature Review

The idea of unit-weighted regression was introduced in 1938 by Samuel Stanley Wilks, a leading statistician who had a special interest in multivariate analysis. Wilks described how unit weights could be used in practical settings, when data were not available to estimate beta weights. For example, a small college may want to select good students for admission. But the school may have no money to gather data and conduct a standard multiple regression analysis. In this case, the school could use several predictors—high school grades, SAT scores, teacher ratings. Wilks showed mathematically why unit weights should work well in practice.

Frank Schmidt in 1971 conducted a simulation study of unit weights. His results showed that Wilks was indeed correct and that unit weights tend to perform well in simulations of practical studies.

Robyn Dawes in 1979 discussed the use of unit weights in applied studies, referring to the robust beauty of unit weighted models. Jacob Cohen in 1990 also discussed the value of unit weights and noted their practical utility. Indeed, he wrote, "As a practical matter, most of the time, we are better off using unit weights" (p. 1306).

Dave Kerby in 2003 showed that unit weights compare well with standard regression, doing so with a cross validation study—that is, he derived beta weights in one sample and applied them to a second sample. The outcome of interest was suicidal thinking, and the predictor variables were broad personality traits. Kerby also showed how Regression Tree analysis could be combined with unit weights to further simplify unit-weighted regression. In this approach, the variate consists of merely the weighted counts of significant predictors.