Day 9: Team A

Discriminant Analysis

In class the discussion was based on:

1.       1^st level of analysis

          Frequencies, Cross tabs, Overlaps

2.       Cluster: K-means and Hierarchical

3.       MDS – Multi Dimensional Scaling (Perceptual Mapping), Overall Similarity, Attribute Based

4.       Factor analysis

5.       Discriminant Analysis

Discriminant Analysis is used primarily to predict membership in two or more mutually exclusive groups. It can be used to assess the adequacy of classification, given the group memberships of the objects under study; or when we wish to assign objects to one of a number of (known) groups of objects. Discriminant function analysis is used to determine which variables discriminate between two or more naturally occurring groups.

Discriminant Analysis may be used for two objectives: either we want to assess the adequacy of classification, given the group memberships of the objects under study; or we wish to assign objects to one of a number of (known) groups of objects. Discriminant Analysis may thus have a descriptive or a predictive objective.

For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide (1) to go to college, (2) to attend a trade or professional school, or (3) to seek no further training or education. For that purpose the researcher could collect data on numerous variables prior to students' graduation. After graduation, most students will naturally fall into one of the three categories. Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students' subsequent educational choice.

The characteristics of discriminate analysis are as follows:

·         Outcome variable or the dependent variable will be a category variable and will assume two values unlike regression.

·         It is a predictive function – can be used to predict whether a variable will belong to a particular group.

·         To do discriminate analysis we must know past data.

·         All the variables used to make the discriminate equation are normally distributed.

Discriminant function analysis is broken into a 2-step process: (1) testing significance of a set of discriminant functions, and; (2) classification. The independent variables are the predictors and the dependent variables are the groups.

The major underlying assumptions of DA are:

·               Observations are a random sample

·               Each variable is normally distributed

·               Each of the allocations for the dependent categories in the initial classification 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 cases can be placed in a group)

The purposes of Discriminant Analysis (DA):

·     To classify cases into groups. Statistical significance tests using chi square enable you to see how well the function separates the groups.

·         To test whether cases are classified as predicted.

·     To investigate differences between groups on the basis of the attributes of the cases, indicating which attributes contribute most to group separation.

·    The descriptive technique successively identifies the linear combination of attributes known as canonical discriminant functions (equations) which contribute maximally to group separation

By:

Ria Sarwal

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