energy (version 1.6.2)

disco: distance components (DISCO)

Description

E-statistics DIStance COmponents and tests, analogous to variance components

Usage

disco(x, factors, distance, index=1.0, R=0, method=c("disco","discoB","discoF")) 
disco.between(x, factors, distance, index=1.0, R=0)

Arguments

x

data matrix or distance matrix

factors

matrix of factor labels or integers (not design matrix)

distance

logical, TRUE if x is distance matrix

index

exponent on Euclidean distance in (0,2]

R

number of replicates for a permutation test

method

test statistic

Value

When method="discoF", disco returns a class disco object, which is a list containing

call

call

method

method

statistic

vector of observed statistics

p.value

vector of p-values

k

number of factors

N

number of observations

between

between-sample distance components

withins

one-way within-sample distance components

within

within-sample distance component

total

total dispersion

Df.trt

degrees of freedom for treatments

Df.e

degrees of freedom for error

index

index (exponent on distance)

factor.names

factor names

factor.levels

factor levels

sample.sizes

sample sizes

stats

matrix containing decomposition

When method="discoB", disco passes the arguments to disco.between, which returns a class htest object.disco.between returns a class htest object, where the test statistic is the between-sample statistic (proportional to the numerator of the F ratio of the disco test.

Details

disco calculates the distance components decomposition of total dispersion and if R > 0 tests for significance using the test statistic disco "F" ratio (default method="disco"), or using the between component statistic (method="discoB"), each implemented by permutation test. In the current release disco computes the decomposition for one-way models only.

References

M. L. Rizzo and G. J. Szekely (2010). DISCO Analysis: A Nonparametric Extension of Analysis of Variance, Annals of Applied Statistics, Vol. 4, No. 2, 1034-1055. http://dx.doi.org/10.1214/09-AOAS245

See Also

edist eqdist.e eqdist.etest ksample.e

Examples

      ## warpbreaks one-way decompositions
      data(warpbreaks)
      attach(warpbreaks)
      disco(breaks, factors=wool, R=99)
      
      ## When index=2 for univariate data, we get ANOVA decomposition
      disco(breaks, factors=tension, index=2.0, R=99)
      aov(breaks ~ tension)
      
      ## Multivariate response
      ## Example on producing plastic film from Krzanowski (1998, p. 381)
      tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
                6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
      gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
                 9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
      opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
                   2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
      Y <- cbind(tear, gloss, opacity)
      rate <- factor(gl(2,10), labels=c("Low", "High"))  
	  
	  ## test for equal distributions by rate
      disco(Y, factors=rate, R=99)     
	  disco(Y, factors=rate, R=99, method="discoB")
      
      ## Just extract the decomposition table
      disco(Y, factors=rate)$stats    
	  
	  ## Compare eqdist.e methods for rate
	  ## disco between stat is half of original when sample sizes equal
	  eqdist.e(Y, sizes=c(10, 10), method="original")
	  eqdist.e(Y, sizes=c(10, 10), method="discoB")

      ## The between-sample distance component
      disco.between(Y, factors=rate)