external {fmdu}

Multidimensional External Unfolding Function

Description

external performs multidimensional external unfolding.

Usage

external(
  x,
  w = NULL,
  fixed = NULL,
  z = NULL,
  MAXITER = 1024,
  FCRIT = 1e-08,
  error.check = FALSE,
  echo = FALSE
)

Arguments

x

an n by m rectangular matrix containing dissimilarities or distances.

w

an identical sized matrix containing nonnegative weights (all ones when omitted).

fixed

fixed column coordinates (m x p).

z

null or initial row coordinates (n by p).

MAXITER

maximum number of iterations (default = 1024).

FCRIT

relative convergence criterion (default = 0.00000001).

error.check

extensive check validity input parameters (default = FALSE).

echo

print intermediate algorithm results (default = FALSE).

Value

x original n by m matrix with dissimilarities or distances.

w original n by m matrix with dissimilarity weights.

fixed original m x p fixed column coordinates.

z final n by p matrix with row coordinates.

d final n by m matrix with distances between rows of z and rows of fixed.

last.iteration final iteration number.

last.difference final function difference used for convergence testing.

mse final mean squared error function value.

rmse final root mean squared error function value.

References

de Leeuw, J., and Heiser, W. J. (1980). Multidimensional scaling with restrictions on the configuration. In P.R. Krishnaiah (Ed.), Multivariate analysis (Vol. 5, pp. 501–522). Amsterdam, The Netherlands: North-Holland Publishing Company.

Heiser,W. J. (1987a). Joint ordination of species and sites: The unfolding technique. In P. Legendre and L. Legendre (Eds.), Developments in numerical ecology (pp. 189–221). Berlin, Heidelberg: Springer-Verlag.

Busing, F.M.T.A. (2010). Advances in multidimensional unfolding. Unpublished doctoral dissertation, Leiden University, Leiden, the Netherlands.

Examples

## Not run: 
library( smacof )
data( "breakfast" )
x <- as.matrix( breakfast )
n <- nrow( x )
m <- ncol( x )
d.col <- as.matrix( dist( t( x ) ) )
r <- smacofSym( d.col )
print( r$conf )
e <- external( x, fixed = r$conf )
print( e$z )

## End(Not run)