**Two-Group MultiODA: A Mixed-Integer Linear Programming Solution with Bounded M**

Robert C. Soltysik, M.S., and Paul R. Yarnold, Ph.D.

Optimal Data Analysis, LLC

Prior mixed-integer linear programming procedures for obtaining two-group multivariable optimal discriminant analysis (MultiODA) models require estimation of the value of a parameter, *M*. A new formulation is presented which establishes a lower bound for *M*, which executes more quickly than prior formulations. A sufficient condition for the nonexistence of classification gaps and ambiguous solutions, optimal weighted classification, use of nonlinear terms, selecting an optimal subset of attributes, and aggregation of duplicate observations are discussed. When the design involves six or fewer binary attributes, MultiODA models may easily be obtained for massive samples.