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Linear Discriminant Analysis (LDA)

Linear Discriminant Analysis (LDA). Goal . To classify observations into 2 or more groups based on k discriminant functions (Dependent variable Y is categorical with k classes.) Assumptions Multivariate Normal Distribution variables are distributed normally within the classes/groups.

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Linear Discriminant Analysis (LDA)

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  1. Linear Discriminant Analysis (LDA)

  2. Goal • To classify observations into 2 or more groups based on k discriminant functions (Dependent variable Y is categorical with k classes.) • Assumptions • Multivariate Normal Distribution variables are distributed normally within the classes/groups. • Similar Group Covariances Correlations between and the variances within each group should be similar.

  3. Dependent Variable • Must be categorical with 2 or more classes (groups). • If there are only 2 classes, the discriminant analysis procedure will give the same result as the multiple regression procedure.

  4. Independent Variables • Continuous or categorical independent variables • If categorical, they are converted into binary (dummy) variables as in multiple linear regression

  5. Output Example: Assume 3 classes (y=1,2,3) of the dependent.

  6. Binary Dependent - Regression If only 2 classes of dependent, can do multiple regression Sample data shown below:

  7. Regression Output

  8. Classification Classification Rule in this case: If Pred. Y > 0.5 then Class = 1; else Class = 0. This model yielded 2 misclassifications out of 24. How good is R-square?

  9. Crosstab of Pred. Y and Y For large datasets, one can format the Predicted Y variable and create a crosstab with Y to see how accurately the model classifies the data (fictitious results shown here). The Good and Bad columns represent the number of actual Y values.

  10. Kolmogorov-Smirnov Test Use the crosstabs shown in last slide to conduct the KS Test to determine • Cutoff score, • Classification accuracy, and • Forecasts of model performance.

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