A Generalized Multi-Group Discriminant Function Procedure for Classification: an Application To Ten Groups Of Yam Species

Abstract

Multivariate Analysis (MVA) is based on the Statistical principle of Multivariate Statistics which involves observation and analysis of more than one Statistical outcome variables at a time. Classification in Multivariate analysis deals with developing a statistical rule for allocating observation to one or more groups. A closely associated multivariate technique is discriminant analysis which predicts group membership for an observation. Fishers (1936) developed a technique (Fishers Linear Discriminant Function) that optimally discriminate only two groups. The challenges of developing a mathematical based procedure with some underlying distribution for multiple groups have remained a task to be accomplished as it only exist in theory but not in practice. Owing to these challenges, this work introduces and suggests a mathematical procedure that is based on combinatorial analysis which gave rise to All Possible Pair of functions and allocation rules for a multiple group case. The developed procedure was generalized and applied to both real and simulated data. The developed procedure gave a higher accuracy rate for the real and simulated data under various sample sizes when compared with other conventional methods. It is therefore recommended that the All Possible Pair procedure could be a better approach in situations of any multivariate data structure.

Key Words: Discriminant, Function, Classification, combination, Accuracy Rate.