Multivariate Analysis

9.

Discriminant Analysis

9.1.

Discriminant Analysis Objectives

9.1.1.

Group Classification

9.1.2.

Group Separation

9.1.3.

Dimension Reduction

9.2.

Types of Discriminant Analysis

9.2.1.

Descriptive Discriminant Analysis

9.2.2.

Predictive Discriminant Analysis

9.2.3.

Two-Group Analysis

9.2.4.

Multiple-Group Analysis

9.3.

Discriminant Function Development

9.3.1.

Linear Discriminant Function

9.3.2.

Quadratic Discriminant Function

9.3.3.

Fisher's Linear Discriminant

9.4.

9.4.1.

Multivariate Normality

9.4.2.

Equal Covariance Matrices

9.4.3.

Independence of Observations

9.4.4.

Linear Relationships

9.5.

Two-Group Discriminant Analysis

9.5.1.

Discriminant Function Derivation

9.5.2.

Group Centroids

9.5.3.

Classification Rule

9.5.4.

Cutting Score Determination

9.6.

Multiple-Group Discriminant Analysis

9.6.1.

Number of Discriminant Functions

9.6.2.

Canonical Discriminant Functions

9.6.3.

Eigenvalue Problem

9.6.4.

Successive Extraction

9.7.

Interpretation of Results

9.7.1.

Standardized Discriminant Coefficients

9.7.2.

Structure Matrix

9.7.3.

Group Centroids

9.7.4.

Territorial Map

9.8.

Classification Procedures

9.8.1.

Classification Functions

9.8.2.

Posterior Probabilities

9.8.3.

Prior Probabilities

9.8.4.

Classification Rules

9.9.

Validation and Accuracy Assessment

9.9.1.

9.9.2.

Confusion Matrix

9.9.3.

Cross-Validation

9.9.3.1.

9.9.3.2.

9.9.4.

Press's Q Statistic

9.10.

Stepwise Discriminant Analysis

9.10.1.

Variable Selection Criteria

9.10.2.

Forward Selection

9.10.3.

Backward Elimination

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10. Logistic Regression