modified ant analysis

8/8/2019 Modified ant Analysis

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Discriminant Analysis

Project Members:

Arundati Puranik

Ankita Petiwale

Ankit Pandya

Harshit Desai

Shailee Shah

Pratik Balakrishnan

Faculty : Prof Deepa Dixit


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DEFINITION

It is a statistical technique which allows us to study the

differences between two or more groups of objects withrespect to several variables simultaneously.

Some Applications:

Lending loans to a prospective clients based on their

available information

To classify goods as good or defective ,etc.

To classify medicines as effective and not effective.


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INTRODUCTION

The main purpose of a discriminant function analysis is to

predict group membership based on variables.

Second purpose of DA is understanding the data set, as a

careful examination of the prediction model that can give insight

into the relationship between group membership.


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Formulae

The Discriminant function can be written as:

D1=1 x1 +2 x2 +3 x3++c

Where D1= Discriminant factor (Used to predict the

independent variables)

X1,x2, etc= Discriminant variable(predictor variables)

1, 2, etc= Discriminant coefficients.

similarly we can have

D2 =1 x1 +2 x2 +3 x3+ +c as another discriminant factor.

and

D*=(D1+D2)/2

where D* is the Mean discriminant factor

All the values which are more than D* go into group D1 and the ones

which are less than D* go into group D2.


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Objectives

To determine, amongst many ,which specific variablesaccount most for such intergroup differences.

To find the linear combinations of predictor variables that

enable us to represent the groups.

To establish procedures for assigning new observation to one

or more groups, assuming it fits into atleast one of them.


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EXAMPLE

The following example outlines the creation of a data set

and the use of discriminant analysis.

A director of operations has been plagued with the same

problem for months.


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Example:Random Product Sample AgainstCustomer Returns


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Discriminant Analysis of Normal and Returned

Products

Put Into Group 0 1

0 22 1

1 2 7

Total N 24 8

N correct 22 7

Proportion 91.67 87.5True Copy:

N=32 N correct=29 Proportion

Correct=90.63

Linear Discriminant function :

0 1

Constant -12.6 -23.607C2 1.546 1.026

C3 3.683 5.741

Customer return membership function: -

23.6 + 1.03 (length) + 5.7 (weight)

Normal part membership function: -

12.6 + 1.5 (length) + 3.6 (weight)


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Confusion Matrix

Used to summarize the number of correct and incorrect

classifications that are obtained by Discriminant function.

Difficult to assess these costs individually

The ratio is important to measure the cost of

misclassification


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Limitations

The weights/significance assigned to the variables aresubject to different philosophies.

The analysis is not validated by testing their efficacy with a

fresh sample of entities.

There are two methods of calculating DA, which are

Classification and Predictive Analysis, which creates a

dilemma as to which one to implement.

To optimize DA, there are not many tools available. So the

accuracy of the obtained result is not full-proof. Hence DA

is not very widely used.


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References

www.isixsigma.com

www.referenceforbusiness.com

Statistical Methods In Business and Social

Sciences GV Shenoy, Madan Pandt.


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