LLAsimvar {LLAhclust}R Documentation

Computes similarities among variables using the likelihood linkage analysis approach

Description

Computes similarities among variables using the likelihood linkage analysis approach proposed by Lerman. The likelihood linkage analysis method mainly consists in replacing the value of the estimated similarity coefficient between two variables by the probability of finding a lower value under the hypothesis of stochastic independence, called absence of link in that context. Nine similarity coefficients can be computed using the LLAsimvar function.

Usage

LLAsimvar(x, method = "LLAnumerical", upper = FALSE,
                 simulated.distribution = NULL)

Arguments

x a numeric matrix or data frame.
method Can be one of LLAnumerical, LLAcategorical, LLAordinal, LLAboolean, chi.square, pearson.abs, spearman.abs, kendall.abs or empirical.copula. The methods LLA* were initially defined by Lerman (see references below). The four remaining methods compute the similarity between two variables as one minus the p-value obtained from a test of independence. See the last reference and the example section below for more details.
upper logical value indicating whether the upper triangle of the similarity matrix should be printed by print.LLAsim.
simulated.distribution Object of class empcopula.simulation. Should be set only if the method empirical.copula is selected. See function empcopula.simulate and the example section below for more details.

Details

The following functions are also defined for objects of class LLAsim: names.LLAsim, format.LLAsim, as.matrix.LLAsim and print.LLAsim.

Value

Returns an object of class LLAsim whose attributes are very similar to those of objects of class dist. See dist for more details.

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.

P. Deheuvels (1979), La fonction de dépendance empirique et ses propriétés: un test non paramétrique d'indépendance, Acad. Roy. Belg. Bull. Cl. Sci. 5th Ser. 65, 274-292.

C. Genest and B. Rémillard (2004). Tests of independence and randomness based on the empirical copula process. Test, 13, 335-369.

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

See Also

as.LLAsim,
empcopula.simulate,
LLAsimobj,
LLAhclust,
LLAparteval,
dist.

Examples

data(USArrests)

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

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

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

## Compute similarities between variables using the test of
## independence e la Deheuvels based on the empirical copula
## process recently studied by Genest and Remillard:
s <- LLAsimvar(USArrests, method = "empirical.copula")
s

## The previous computation could have been done in two steps:
d <- empcopula.simulate(n=50,N=2000)
s <- LLAsimvar(USArrests, method = "empirical.copula",
                       simulated.distribution = d)
s

[Package LLAhclust version 0.2-2 Index]