Discriminant Function Analysis

Discriminant Function Analysis determines

which variables distinguish between two or more categorical groups based on their independent variables

Discriminant Analysis Assumptions

• Normal distribution

• Equal variance

• Linear separability of data

DFA uses

Categorical dependent variables with continuous independent variables (use of correspondence analysis)

Discriminant Analysis can be considered

A more powerful version of logistic regression

DFA uses variables from

Known groups to build the model

If group membership is unknown

Use a cluster analysis to attempt to determine group membership

DFA Advantages

• simple and efficient

• Works with large numbers of features

• Can work with more than two variables

DFA Limitations

• assumes normal distribution

• Assumes equal variance

• Assumes linear separability

• May have issues with higher dimensional data

How does Linear DFA work?

• separates data used both axes to generate a new axis

• Minimizes variation and maximizes distance between means

• Transforms data along new axis and maximizes separation through the projection of data along the line

A Discriminant function is a

Weighted average of the values of the independent variables

How are weights selected for a DFA

They are selected so the resulting weighted averages(s) maximize the separation of the observations into the groups (high values come from one group and low values come from another)

Stepwise Selection

• helps select only the best variables to use in our model

• Includes multiple regression

Forward Stepwise Analysis

• A model is built step-by-step

• Variables are evaluated to determine which will contribute most to the discrimination between groups

• Variable that contributes most is included in the model

Backward Stepwise Analysis

• a model is built step-by-step

• Variables are included and at each step they are evaluated to determine which contributes the least to discrimination of the groups

• Variable that contributes the least will be excluded from the model