discrim
object.
discrim
objects.
anova.discrim(object, ...)
discrim
object constructed by the discrim function.
anova.discrim
object.
Objects of this class have the following methods:
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.
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.
# 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)