permtest.smacof: SMACOF Permutation

In smacof: Multidimensional Scaling

SMACOF Permutation

Description

These methods perform a permutation test for a symmetric or an unfolding SMACOF model.

Usage

## S3 method for class 'smacof'
permtest(object, data,  method.dat = "pearson", nrep = 100, verbose = TRUE, ...)
## S3 method for class 'smacofR'
permtest(object, data = NULL,  method.dat = "rows", nrep = 100, verbose = TRUE, ...)
## S3 method for class 'smacofPerm'
plot(x, alpha = 0.05, main, xlab, ylab, ...)

Arguments

object	Object of class "smacofB", i.e., an MDS solution from smacofSym()
data	Optional argument; if provided permutations are performed on the data matrix (see details; ignored for unfolding models)
method.dat	If data are provided, this must be one of "pearson", "spearman", "kendall", "euclidean", "maximum", "manhattan", "canberra", "binary". For unfolding models it is either "full" for full permutations or "rows" for permutations within rows.
nrep	Number of permutations
verbose	If TRUE, permutation index is printed out
x	Object of class "smacofPerm"
alpha	Alpha level
main	Plot title.
xlab	Label of x-axis.
ylab	Label of y-axis.
...	additional plot arguments for plot function; additional arguments to be passed to sim2diss in permutation functions.

Details

This routine permutes m dissimilarity values, where m is the number of lower diagonal elements in the corresponding dissimilarity matrix. For each sample a symmetric, nonmetric SMACOF of dimension ndim is computed and the stress values are stored in stressvec. Using the fitted stress value, the p-value is computed. Subsequently, the empirical cumulative distribution function can be plotted using the plot method.

If the MDS fit provided on derived proximities of a data matrix, this matrix can be passed to the permtest function. Consequently, the data matrix is subject to permutations. The proximity measure used for MDS fit has to match the one used for the permutation test. If a correlation similarity is provided, it is converted internally into a dissimilarity using sim2diss with corresponding arguments passed to the ... argument.

Value

stressvec	Vector containing the stress values of the permutation samples
stress.obs	Stress (observed sample)
pval	Resulting p-value
call	Model call
nrep	Number of permutations
nobj	Number of objects

Author(s)

Patrick Mair and Ingwer Borg

References

Mair, P., Borg, I., and Rusch, T. (2016). Goodness-of-fit assessment in multidimensional scaling and unfolding. Multivariate Behavioral Research, 51, 772-789. doi: 10.1080/00273171.2016.1235966

Mair, P, Groenen, P. J. F., De Leeuw, J. (2022). More on multidimensional scaling in R: smacof version 2, Journal of Statistical Software, 102(10), 1-47. doi: 10.18637/jss.v102.i10

See Also

jackmds, bootmds

Examples

## permuting the dissimilarity matrix (full)
data(kinshipdelta)
fitkin <- mds(kinshipdelta, ndim = 2, type = "interval")
set.seed(222)
res.perm <- permtest(fitkin)
res.perm
plot(res.perm)

## permuting the data matrix
GOPdtm[GOPdtm > 1] <- 1     ## use binary version
diss1 <- dist(t(GOPdtm[,1:10]), method = "binary")  ## Jaccard distance
fitgop1 <- mds(diss1, type = "ordinal")
fitgop1
set.seed(123)
permtest(fitgop1, GOPdtm[,1:10], nrep = 10, method.dat = "binary")

rmat <- cor(GOPdtm[,1:10], method = "kendall")  ## Kendall correlation
diss2 <- sim2diss(rmat, method = 1)
fitgop2 <- mds(diss2, type = "ordinal")
fitgop2
set.seed(123)
permtest(fitgop2, GOPdtm[,1:10], nrep = 10, method.dat = "kendall", method = 1)

## unfolding permutation
data(breakfast)
res.unfolding <- unfolding(breakfast, ndim = 2)
set.seed(123)
permtest(res.unfolding, nrep = 20, method.dat = "rows")

smacof documentation built on May 6, 2022, 9:05 a.m.