bootmds.smacofB: SMACOF Bootstrap

In smacof: Multidimensional Scaling

SMACOF Bootstrap

Description

Performs a bootstrap on a SMACOF solution. It works for derived dissimilarities only. The original data matrix needs to be provided, as well as the type of dissimilarity measure used to compute the input dissimilarities.

Usage

## S3 method for class 'smacofB'
bootmds(object, data,  method.dat = "pearson", nrep = 100, 
alpha = 0.05, verbose = FALSE, ...)

## S3 method for class 'smacofboot'
plot(x, plot.dim = c(1,2), col = 1, 
label.conf = list(label = TRUE, pos = 3, cex = 0.8), 
ell = list(lty = 1, lwd = 1, col = "gray"), main, xlab, ylab, xlim, ylim, 
asp = 1, type = "p", pch = 20, ...)

Arguments

object	Object of class "smacofB", i.e., an MDS solution from mds().
data	Initial data (before dissimilarity computation).
method.dat	Dissimilarity computation used as MDS input. 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 bootstrap replications.
alpha	Alpha level for confidence ellipsoids.
verbose	If TRUE, bootstrap index is printed out.
...	Additional arguments needed for dissimilarity computation as specified in sim2diss().
x	Object of class "smacofboot"
plot.dim	Vector with dimensions to be plotted.
col	Color for points.
label.conf	List with arguments for plotting the labels of the configurations in a configuration plot (logical value whether to plot labels or not, label position). If pos = 5 labels are placed away from the nearest point.
ell	List with arguments for plotting ellipses: line type, line width, color.
main	Plot title.
xlab	Label of x-axis.
ylab	Label of y-axis.
xlim	Scale x-axis.
ylim	Scale y-axis.
asp	Aspect ratio.
pch	Plotting symbol for object point.
type	Type of plot.

Details

In order to examine the stability solution of an MDS, a bootstrap on the raw data can be performed. This results in confidence ellipses in the configuration plot. The ellipses are returned as list which allows users to produce (and further customize) the plot by hand.

Value

cov	Covariances for ellipse computation
bootconf	Configurations bootstrap samples
stressvec	Bootstrap stress values
bootci	Stress bootstrap percentile confidence interval
stab	Stability coefficient

References

Jacoby, W. G., & Armstrong, D. A. (2014). Bootstrap confidence regions for multidimensional scaling solutions. American Journal of Political Science, 58, 264-278.

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

Examples

## Example using Euclidean distances
data <- na.omit(PVQ40[,1:5])
diss <- dist(t(data))   ## Euclidean distances 
fit <- mds(diss)        ## 2D interval MDS

set.seed(123)
resboot <- bootmds(fit, data, method.dat = "euclidean", nrep = 50)
resboot
plot(resboot)

## Example using Pearson correlations 
sim <- cor(data)
diss <- sim2diss(sim, method = 1)  ## subtract from 1 (method needs to be passed to bootmds)
fit <- mds(diss, type = "ratio", ndim = 3)        ## 3D ratio MDS

set.seed(123)
resboot <- bootmds(fit, data, method.dat = "pearson", nrep = 50, alpha = 0.1, method = 1)
resboot
## plot 1st against 3rd dimension
ellipses <- plot(resboot, plot.dim = c(1,3), ell = list(lty = 2, col = "gray", lwd = 0.8))
str(ellipses)  ## list of ellipse coordinates for each object

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