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:
n is the number of cases q is the number of groups p is the number of variables