Wilks' lambda
Discriminant function analysis is used to determine which continuous variables discriminate between two or more naturally occurring groups.Discriminant function analysis is multivariate analysis of variance (MANOVA) reversed. In MANOVA, the independent variables are the groups and the dependent variables are the predictors.In BA, the independent variables are the predictors and the dependent variables are the groups.
Everitt & Dunn (1991) and Polit (1996) provide more detail about the use and interpretation of Wilks' lambda.
Wilks' lambda is a test statistic used in multivariate analysis of variance (MANOVA) to test whether there are differences between the means of identifed groups of subjects on a combination of dependent variables.Wilks' lambda performs, in the multivariate setting, with a combination of dependent variables, the same role as the F-test performs in one-way analysis of variance. Wilks' lambda is a direct measure of the proportion of variance in the combination of dependent variables that is unaccounted for by the independent variable. If a large proportion of the variance is accounted for by the independent variable then it suggests that there is an effect from the grouping variable and that the groups have different mean values. Wilks' lambda statistic can be transformed (mathematically adjusted) to a statistic which has approximately an F distribution. This makes it easier to calculate the P-value. Often authors will present the F-value and degrees of freedom, as in the above paper, rather than giving the actual value of Wilks' lambda.
There are a number of alternative statistics that can be calculated to perform a similar task to that of Wilks' lambda, such as Pillai's trace criterion and Roy's gcr criterion; however, Wilks' lambda is the most widely used.
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Rohan Moon
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