The multiple comparisons method for the discrim object.

DESCRIPTION:

Computes Hotelling's T squared statistics for all pairs of groups and for each group pair computes confidence intervals for the differences between means of the p-variate feature vectors.

USAGE:

multicomp.discrim(x, alpha=0.05, significant.only=T, ...) 

REQUIRED ARGUMENTS:

x
a discrim object constructed by the discrim function.

OPTIONAL ARGUMENTS:

alpha
a floating point variable between 0 and 1 specifying the significance level for the T squared tests. For T squared tests with corresponding F statistic p-values less than alpha, multiple comparisons are computed between the means of the p-variate feature vectors for those two groups.

VALUE:

a multicomp.discrim object.

METHODS:

Objects of this class have the following methods:

ARGUMENTS:

print
the print method.

STRUCTURE:

The structure of a multicomp.discrim object is a list with the following data members.

ARGUMENTS:

hotellings.T2
a data frame containing the Hotelling's T squared statistics.
multiple.comparisons
a list of multicomp objects. A multicomp object will exist for each significant T squared statistic in the hotellings.T2 data member.

DETAILS:

Computes Hotelling's T squared statistics for all pairs of groups. For T squared tests that have a significant F statistic, confidence intervals are computed for the difference between the p-variate means of the feature data for those two groups using multiple comparison techniques to control the family-wise error rate (Hsu, 1996). See multicomp.default for details.

When the covariance matrices for each group are not equal the covariance for the difference between the two p-variate mean vectors is taken to be the sum of the two covariance matrices weighted by the inverse of the group sample size. Yao's approximation to the second degrees of freedom for the corresponding F statistic is used (Seber, 1984, p.115). This covariance and degrees of freedom are also used in computing the pairwise confidence intervals for the p means if the F statistic is significant. These correspond to the vmat and df.residual in multicomp.default.

REFERENCES:



Hsu, J. C. (1996). Multiple Comparisons Theory and Methods, Chapman & Hall.

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") 
multicomp(flea.spher)