fastmdu {fmdu}

(Restricted) Multidimensional Unfolding Function

Description

fastmdu performs three types of multidimensional unfolding in different combination for row and column objects. The function follows algorithms given by de Leeuw and Heiser (1980), Heiser (1987), and Busing (2010).

Usage

fastmdu(
  delta,
  w = NULL,
  p = 2,
  x = NULL,
  rx = NULL,
  y = NULL,
  ry = NULL,
  MAXITER = 1024,
  FCRIT = 1e-08,
  error.check = FALSE,
  echo = FALSE
)

Arguments

delta

an n by m rectangular matrix containing dissimilarities.

w

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

p

dimensionality (default = 2).

x

either initial or fixed row coordinates (n by p) or independent row variables (n by hx).

rx

Row restriction. If omitted, x is free and x contains the initial row coordinates. If logical valued, x (n by p) contains the initial row coordinates and rx (n by p) indicates free (false) and fixed (true) row coordinates. If real valued, x (n by hx) contains hx independent row variables and rx (hx by p) contains the initial row regression coefficients.

y

either initial or fixed column coordinates (m by p) or independent column variables (n by hy).

ry

Column restriction. If omitted, y is free and y contains the initial column coordinates. If logical valued, y (m by p) contains the initial column coordinates and ry (m by p) indicated free (false) and fixed (true) column coordinates. If real valued, y (n by hy) contains hy independent column variables and ry (hy by p) contains the initial column regression coefficients.

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

data original n by m matrix with dissimilarities.

weights original n by m matrix with dissimilarity weights.

row.coordinates final n by p matrix with row coordinates.

col.coordinates final m by p matrix with column coordinates.

row.coefficients if rx is real valued, final hx by p matrix with row regression coefficients.

col.coefficients if ry is real valued, final hy by p matrix with column regression coefficients.

distances final n by m matrix with distances.

last.iteration final iteration number.

last.difference final function difference used for convergence testing.

n.stress final normalized stress value.

stress.1 final stress-1 value.

call function call

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" )
breakfast <- as.matrix( breakfast )
n <- nrow( breakfast )
m <- ncol( breakfast )
p <- 2
w <- matrix( 1, n, m )
x <- matrix( runif( n * p ), n, p )
y <- matrix( runif( m * p ), m, p )
r <- fastmdu( breakfast, w, p, x, NULL, y, NULL )
print( r )

## End(Not run)