LLAparteval {LLAhclust}R Documentation

Evalutes the quality of each partition compatible with a hierarchy in terms of several indices

Description

Evalutes the quality of each partition compatible with the hierarchy returned by LLAhclust . If the hierarchy is obtained from similarity coefficients computed using LLA* methods, the global and local statistics proposed by Lerman are calculated. Otherwise, for similarity coefficients obtained from independence tests (see LLAsimvar), for each partition, the inter-class p-values are combined using Tippett's and Fisher's rules. Furthermore, the minimum inter-class p-value and the maximum intra-class p-value are given. See the last reference and the examples below for more details.

Usage

LLAparteval(tree, s, m=NULL)

Arguments

tree An object of class hclust as returned by LLAhclust.
s An object of class LLAsim as returned by LLAsimvar, LLAsimobj or as.LLAsim.
m Integer. If set, the quality of the m coarsest partitions only is evaluated.

Value

Returns a data.frame whose columns are: global.stat and local.stat if the hierarchy is obtained from similarity coefficients computed using LLA* methods, and tippett.inter, fisher.inter, min.inter and max.intra in case of similarity coefficients obtained from independence tests.

References

I.C. Lerman (1981), Classification et analyse ordinale de donnés, Dunod, Paris.

I.C. Lerman (1991), Foundations of the likelihood linkage analysis classification method, Applied Stochastic Models and Data Analysis, 7, pages 63–76.

I.C. Lerman (1993), Likelihood linkage analysis classification method: An example treated by hand, Biochimie, 75, pages 379–397.

I.C. Lerman, Ph. Peter and H. Leredde (1993), Principes et calculs de la méthode implantée dans le programme CHAVL (Classification Hiérarchique par Analyse de la Vraisemblance des Liens), Modulad, 12, pages 33-101.

I. Kojadinovic (2007), Hierarchical clustering of continuous variables based on the empirical copula process, submitted.

See Also

LLAsimvar,
LLAsimobj,
as.LLAsim,
LLAhclust.

Examples


data(USArrests)

## Compute similarities between variables based on
## the LLAnumerical method:
s <- LLAsimvar(USArrests)
s

## Perform the hierarchical clustering of the variables:
h <- LLAhclust(s)
plot(h)

## Compute the quality of the partitions compatible
## with the hierarchy in terms of the statistics defined by Lerman:
LLAparteval(h,s)

## Compute similarities between variables using the classical
## bilateral test of independence based on Spearman's rho:
s <- LLAsimvar(USArrests, method = "spearman.abs")
s

## Perform the hierarchical clustering of the variables
## using Fisher's p-value combination method:
h <- LLAhclust(s,method="fisher")
plot(h)
## NB: the height in the dendrogram is a p-value
## and can be used to identify mutually independent classes of
## variables, if any.

## Compute the quality of the partitions compatible
## with the hierarchy in terms of the indices defined in the
## last reference:
LLAparteval(h,s)

[Package LLAhclust version 0.2-2 Index]