smacof (version 2.1-7)

jackmds: SMACOF Jackknife

Description

These methods perform a SMACOF Jackknife and plot the corresponding solution.

Usage

# S3 method for smacofB
jackmds(object, eps = 1e-6, itmax = 100, verbose = FALSE)
# S3 method for smacofJK
plot(x, plot.dim = c(1,2), hclpar = list(c = 50, l = 70), 
col.p, col.l, plot.lines = TRUE, legend = FALSE, inset = c(-0.2, 0), cex.legend = 0.7,
main, xlab, ylab, xlim, ylim, asp = 1, ...)

Value

smacof.conf

SMACOF configurations

jackknife.conf

An array of n-1 configuration matrices for each Jackknife MDS solution

comparison.conf

Centroid Jackknife configurations (comparison matrix)

stab

Stability measure

cross

Cross validity

disp

Dispersion

loss

Value of the loss function

ndim

Number of dimensions

call

Model call

niter

Number of iterations

nobj

Number of objects

Arguments

object

Object of class "smacofB", i.e., an MDS solution from smacofSym()

itmax

Maximum number of iterations

eps

Convergence criterion

verbose

If TRUE, intermediate stress is printed out

x

Object of class "smacofJK"

plot.dim

Vector with dimensions to be plotted.

hclpar

Chroma and luminance to be used for HCL colors (further details see rainbow_hcl)

col.p

Point color. If omitted, hcl colors will be used; if specified, the corresponding (single) color will be used for plotting.

col.l

Line color. If omitted, hcl colors will be used; if specified, the corresponding (single) color will be used for plotting.

plot.lines

If TRUE, the Jackknife configurations are plotted are connected with their centroid.

legend

If TRUE, the centroid labels are added as legend.

inset

Inset distance from the margins as a fraction of the plot region when legend is placed by keyword.

cex.legend

Character expansion factor for legend.

main

Plot title.

xlab

Label of x-axis.

ylab

Label of y-axis.

xlim

Scale x-axis.

ylim

Scale y-axis.

asp

Aspect ratio.

...

Further plot arguments passed: see plot for detailed information.

Author

Jan de Leeuw and Patrick Mair

Details

In order to examine the stability solution of an MDS, a Jackknife on the configurations can be performed (see de Leeuw & Meulman, 1986) and plotted. The plot shows the jackknife configurations which are connected to their centroid. In addition, the original smacof configuration (transformed through Procrustes) is plotted. The Jackknife function itself returns also a stability measure (as ratio of between and total variance), a measure for cross validity, and the dispersion around the original smacof solution.

References

De Leeuw, J., & Meulman, J. (1986). A special jackknife for multidimensional scaling. Journal of Classification, 3, 97-112.

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. tools:::Rd_expr_doi("10.18637/jss.v102.i10")

See Also

bootmds

Examples

## symmetric smacof
data <- na.omit(PVQ40[,1:5])
diss <- dist(t(data))   ## Euclidean distances 
fit <- mds(diss) 
res.jk <- jackmds(fit)

plot(res.jk, col.p = "black", col.l = "gray")
plot(res.jk, hclpar = list(c = 80, l = 40))
plot(res.jk, hclpar = list(c = 80, l = 40), plot.lines = FALSE)