Discriminant Function Analysis Notes and Technical Information - Formulas

The formulas for computing the Mahalanobis distances and classification of cases, given a-priori probabilities, are described in Lindeman, Merenda, and Gold (1980, Chapter 6). Detailed descriptions of computational formulas and examples are also presented in, for example, Cooley and Lohnes (1971, Chapters 9 and 10) and Pedhazur (1973, Chapters 17 and 18).

Wilk's Lambda
The Wilks' Lambda statistic for the overall discrimination is computed as the ratio of the determinant (det) of the within-groups variance/covariance matrix over the determinant of the total variance covariance matrix:

Wilk's Lambda = det(W)/det(T)

The F approximation to Wilks' Lambda is computed following Rao (1951).

Partial Lambda
The partial Lambda is computed as the multiplicative increment in lambda that results from adding the respective variable:

partial Lambda = Lambda(after)/Lambda(before)

Put another way, the partial Lambda is the ratio of Wilks' Lambda after adding the respective variable over the Wilks' Lambda before adding the variable.

The corresponding F statistic (see Rao, 1965, 0. 470) is computed as:

F = [(n-q-p)/(q-1)]*[(1-partial lambda)/partial lambda]

Where:

nis the number of cases
qis the number of groups
pis the number of variables