Multivariate Analysis

In: Business and Management

Submitted By priyanshigupta
Words 6778
Pages 28
Multivariate Discriminant Analysis
Priyanshi Gupta

An Overview
 MDA is a statistical technique used to classify an observation into one of the several a priori groupings dependent on the observation’s individual characteristics. It is used primarily to classify and/or make predictions in the problems where dependent variable comes in qualitative form, for example, male or female, bankrupt or non-bankrupt etc.  So the first step is to establish explicit group classifications. We have got observations coming from k groups. We are trying to look at what is the best way or best function in order to discriminate observations coming from different groups.

 Once such function is in place, we go to classification which basically is the problem of classification of a new observation into appropriate population using the discriminant function.
 So typically in such problems, once you have a set of data (called LEARNING set of data) with observations possibly coming from different populations are pre-classified, having predefined memberships to the groups. And based on the particular previously classified data, we create a discriminant function and can use it after proper calibration to classify a new observation to be coming from one of the groups.  Discriminant analysis is used when groups are known a priori.

Types of DA Problems

 2 Group Problems...
…regression can be used

 k-Group Problem (where k>=2)...
…regression cannot be used if k>2

Example of a 2-Group DA Problem: ACME Manufacturing
 All employees of ACME manufacturing are given a pre-employment test measuring mechanical and verbal aptitude.

 Each current employee has also been classified into one of two groups: satisfactory or unsatisfactory.
 We want to determine if the two groups of employees differ with respect to their test scores.  If so, we want to develop a rule for…...

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