1. Discriminant Analysis Susan Kolenko Feb. 26, 2009 STAT 8320

2. Review Objectives of Discriminant Analysis Example using SAS Tonight’s Program:

4. Introduction and Review • Discriminant Analysis is appropriate for what type of Response variables? • NOMINAL CATEGORICAL • What type of Explanatory variables? • ONE OR MORE THAT ARE METRIC • Discriminant Analysis is what as compared to a MANOVA : • The reverse of a MANOVA • Response and Explanatory Variables change functions

5. Similar to Cluster Analysis, but what’s different? • Discriminant Analysis requires what kind of knowledge of the classes or group memberships? • A priori • PROC DISCRIM uses what approach to Discriminant Analysis? • Fisher’s Approach • By default, PROC DISCRIM estimates a separate discriminant function for each group in the class variable

6. A Typical Discriminant Analysis has THREE Objectives

7. Objective 1: • Is to identify the variables that best discriminate between the groups • Variables that provide the best discrimination are called what kind of variables? • Discriminator Variables

8. Objective 2: • Is to use the identified variables to develop an equation for computing an index to represent the differences between the 2 groups • The discriminant function is what kind of a combination of the original quantitative variables? • Linear

9. Objective 3: • Is to classify future observations into one of the two groups • The discriminant function forms the discriminant scores. The new variable generated by a discriminant analysis is described as: • Z = w1 x ExplVar1 + w2 x ExplVar2 • W = discriminant weights

10. Evaluating the Significance of Discriminating Variables • The null and alternative hypothesis are: • Ho : µ 1 = µ 2 • H1 : µ 1 ≠ µ 2 • There’s no surprise here !

11. The probability of any random observation belonging to a certain group is called: • Prior probability • We’ll see in our example, the probability found in gender is: • 0.5 (either boy or girl) • Often the priors are assumed to be what? • Equal

12. Estimate of the Discriminant Function • We saw earlier that: • Z = constant +w1 x ExplVar1 + w2 x ExplVar2 • A constant (the intercept) is added to the unstandardized discriminant function so that the average of the discriminant scores is zero. • The constant adjusts the scale of the discriminant score.

13. Let’s start our example using the STUDENT dataset