Team G Day 9 DISCRIMINANT ANALYSIS- Malovika Roy

DISCRIMINANT ANALYSIS



DA involves the determination of a linear equation like regression that will predict which
group the case belongs to. The form of the equation or function is:

D = v1X1 + v2X2 + v3X3 ....= viXi +  a

Where D = discriminate function
v = the discriminant coeffi cient or weight for that variable
X = respondent’s score for that variable
a = a constant
i = the number of predictor variables


Many interesting variables are categorical, such as political party voting intention, migrant/non-migrant status,making a profit or not, holding a particular credit card, owning, renting or paying a mortgage for a house, employed/unemployed, satisfied versus dissatisfied employees, which customers are likely to buy a product or not buy.


The aim of the statistical analysis in Discriminant Analysis (DA) is to combine (weight) the variable scores in
some way so that a single new composite variable, the discriminant score, is produced.

Similarly, at the end of the DA process, it is hoped that each group will have a normal
distribution of discriminant scores. The degree of overlap between the discriminant score
distributions can then be used as a measure of the success of the technique.


Assumptions of discriminant analysis:-

• The major underlying assumptions of DA are:
• The observations are a random sample.
• Each predictor variable is normally distributed
• Each of the allocations for the dependent categories in the initial classifi cation are correctly classified;
• There must be at least two groups or categories, with each case belonging to only one group so that the groups are mutually exclusive and collectively exhaustive (all casescan be placed in a group);
• Each group or category must be well defined, clearly differentiated from any other group(s) and natural. Putting a median split on an attitude scale is not a natural way form groups. Partitioning quantitative variables is only justifiable if there are easily identifiable gaps at the points of division; for instance, three groups taking three available levels of amounts of housing loan; the groups or categories should be defined before collecting the data;
• The attribute(s) used to separate the groups should discriminate quite clearly between the groups so that group or category overlap is clearly non-existent or minimal;group sizes of the dependent should not be grossly different and should be at least five times the number of independent variables.

There are several purposes of DA:

• To investigate differences between groups on the basis of the attributes of the cases,indicating which attributes contribute most to group separation.
• Predictive DA addresses the question of how to assign new cases to groups. The DA function uses a person’s scores on the predictor variables to predict the category to which the individual belongs.
• To determine the most parsimonious way to distinguish between groups.
• To classify cases into groups. Statistical significance tests using chi square enable you
• To see how well the function separates the groups.
• To test theory whether cases are classified as predicted.

The critical elements to watch out for in case of DA is the classification tables where the groups are finally classified according to the independent variables taken up. To get the perfects score the final equation of the content with the multiple unstandardised coefficients gives the final value or score

Based on these scores we can actually predict the many characteristics or attributes for the same group of people for the future