The ANOVA method for the discrim object.

DESCRIPTION:

Computes multivariate tests for the equivalence of group p-variate means of the training data used to fit the discriminant function, or calculates likelihood ratio, AIC, and BIC for multiple discrim objects.

USAGE:

anova.discrim(object, ...)

REQUIRED ARGUMENTS:

object
a discrim object constructed by the discrim function.

VALUE:

an anova.discrim object.

METHODS:

Objects of this class have the following methods:

ARGUMENTS:

print
the print method.

DETAILS:

For a single discrim object, this anova method will compute Wilks lambda, Pillai trace, Hotelling-Lawley trace, and Roy's greatest root. These one-way multivariate analysis of variance statistics (MANOVA) test the hypothesis that the group p-variate mean vectors for the training data used to fit the discrim function are equal. These tests are only computed if the covariance structure is homoscedastic or spherical, otherwise an error results.

For more than one discrim object, anova.discrim will compute the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), for each discrim object. Also computed are the likelihood ratio tests for each adjacent discrim object in the argument list. Details on using the likelihood ratio tests for finding model parsimony can be found in McLachlan (1992) and references therein. The examples below can give a quick illustration of the concept. For the flea beetles data found in Seber (1984), we fail to reject the null hypothesis that the covariance structure of the bivariate observations from three species of flea beetles' (C.concinna, C.heikertingeri, and C.heptapotamica) is spherical. For the Pima indian data found in Ripley (1996), we fail to reject the hypothesis that the covariance structure for the feature data of the two groups (diabetics and non-diabetics) have the same correlation structure.

REFERENCES:



McLachlan, G. J. (1992). Discriminant Analysis and Statistical Pattern Recognition, John Wiley & Sons.

Ripley, B.D. (1996). Pattern Recognition and Neural Networks, Cambridge University Press.

Seber, G.A.F. (1984). Multivariate Observations, John Wiley & Sons.

SEE ALSO:

, , , , .

EXAMPLES:

# flea beetle data from Seber (1984)
flea.lin <- discrim(species ~ x1 + x2, data=flea.beetles,
    family=Classical("lin"), prior="none")
flea.spher <- discrim(species ~ x1 + x2, data=flea.beetles,
    family=Classical("spher"), prior="none")
anova(flea.spher, flea.lin)
anova(flea.spher)

# Pima indian data from Ripley (1996)
pima.quad <- discrim(type ~ pregnacies + glucose + BP + skin.fold +
    body.mass.index + diabetes.pedigree + age, data=pima,
    family=Classical("heter"), prior="none")
pima.eq <- discrim(type ~ pregnacies + glucose + BP + skin.fold +
    body.mass.index + diabetes.pedigree + age, data=pima,
    family=Classical("equal corr"), prior="none")
pima.prop <- discrim(type ~ pregnacies + glucose + BP + skin.fold +
    body.mass.index + diabetes.pedigree + age, data=pima,
    family=Classical("prop"), prior="none")
anova(pima.prop, pima.eq, pima.quad)