permtest.smacofP function

Permutation test for smacofP objects

Performs a permutation test on an MDS solution. It works with a smacofP object alone and also for derived dissimilarities, i.e. generated by the call dist(data). The original data matrix needs to be provided, as well as the type of dissimilarity measure used to compute the input dissimilarities.

## S3 method for class 'smacofP'
permtest(
  object,
  data,
  method.dat = "pearson",
  nrep = 100,
  verbose = FALSE,
  ...
)

Arguments

• object: Object of class smacofP if used as method or another object inheriting from smacof (needs to be called directly as permtest.smacofP then).
• data: Optional: Initial data; if provided permutations are performed on the data matrix (see details)
• method.dat: Dissimilarity computation used as MDS input. This must be one of "pearson", "spearman", "kendall", "euclidean", "maximum", "manhattan", "canberra", "binary". If data is provided, then this must be provided as well.
• nrep: Number of permutations.
• verbose: If TRUE, bootstrap index is printed out.
• ...: Additional arguments needed for dissimilarity computation as specified in sim2diss.

Returns

An object of class 'smacofPerm', see permtest for details and methods. It has values

• 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

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.

Examples

##see ?smacof::permtest for more
## permuting the dissimilarity matrix (full)
#' data(kinshipdelta)
fitkin <- rStressMin(kinshipdelta, ndim = 2, r=0.5,itmax=10) #use higher itmax
set.seed(222)
res.perm <- permtest(fitkin,nrep=5) #use higher nrep in reality
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 <- alscal(diss1,type="interval",itmax=10) #use higher itmax
fitgop1
set.seed(123)
permtest(fitgop1, GOPdtm[,1:10], nrep = 5, method.dat = "binary")