A statistical technique for the development of an alternate list when using constrained optimization to make admission decisions

In an earlier study it was demonstrated that constrained optimization could be used to accurately translate admission goals. Constrained optimization differs from weighting equations in that it does not assign a rank ordering. Although constrained optimization is conceptually superior, some procedures within the admissions process require a rank ordering of applicants.

The purpose of this study is to describes and evaluate the use of two discriminant analysis procedures to obtain a rank order list by generating weights that model constrained optimization procedures. This study also evaluates the usefulness of an additional method that does not require a rank ordering.

Premium Solver selected a class from the 1998/99 applicant pool. A discriminant analysis was used to generate a discriminant function for modeling the dichotomous group classification selection variable. These weights were then applied and the discriminant function values calculated. The success of the procedure was evaluated by examining rank orders and the magnitude of the correlation and R-square statistic.

Discriminant analysis accounted for 70% of the decision variance generated by the constrained optimization procedure. Using real data allowed an estimate of the number of students impacted by inconsistent outcomes.

Discriminant analysis could be used to manage an alternate list, however it will be based on somewhat different criteria than the initial selection procedure. Each method evaluated has advantages and disadvantages and the selection of one method over another depends on what outcomes are most valued by the college.