Question

how can i find the number of linear discriminant functions? I need to know how i can find out if there is one function, two functions, more? how do i know how many LDF's are there?

Answer 1

The number of linear discriminant functions (LDF’s) required depends upon the number of groups.

The linear discriminant analysis involves categorical dependent or response variable, and continuous independent or predictor variables.

Suppose the categorical dependent variable has k possible groups or classes. Also, consider that there are p independent variables that can be used for the prediction of the dependent variable value (that is, the class of the dependent variable).

Then, the number of linear discriminant functions is min {k – 1, p}, that is, the number of linear discriminant functions is the minimum of one less than the number of possible groups or classes of the dependent variable, and the number of independent predictors.

It must be noted that the linear discriminant functions must be orthogonal to one another.

For example, consider that the dependent variable has 2 possible classes, that is, k = 2. Then, k – 1 = 1.

In order to perform linear discriminant analysis, there must be at least 1 independent continuous predictor, so that, p = 1.

Then, min {k – 1, p} = min {1, 1} = 1. Thus, a 2-group linear discriminant analysis requires one linear discriminant function.