vmu {smacof}

Vector Model of Unfolding

Description

Computes the metric vector model of unfolding (VMU) on rectangular input data (preferences, ratings) with the individuals (rows) represented as vectors in the biplot. There is also the option to fix the column coordinates.

Usage

vmu(delta, ndim = 2, center = TRUE, scale = FALSE, col.coord = NULL)

## S3 method for class 'vmu'
plot(x, ...)

Arguments

delta

Data frame or matrix of preferences, ratings, dissimilarities

ndim

Number of dimensions

center

If TRUE input data are centered row-wise.

scale

If TRUE input data are scaled row-wise.

col.coord

Optional fixed coordinates for the column objects in delta.

x

Object of class "vmu".

...

Additional arguments passed to biplot in stats.

Value

conf.row

Row coordinates

conf.col

Column coordinates

VAF

variance accounted for

Author(s)

Ingwer Borg and Patrick Mair

References

Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling (2nd ed.). Springer.

Borg, I., Groenen, P. J. F., & Mair, P. (2018). Applied Multidimensional Scaling and Unfolding (2nd ed.). Springer.

Tucker, L. R. (1960). Intra-individual and inter-individual multidimensionality. In H. Gulliksen & S. Messick (Eds.), Psychological scaling: Theory and applications (pp. 155-167). Wiley.

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

biplot, unfolding

Examples

## VMU on portrait value questionnaire ratings
fit_vmu <- vmu(PVQ40agg)         ## fit 2D VMU
fit_vmu
plot(fit_vmu, cex = c(1, 0.7))   ## call biplot from stats

## VMU with fixed column coordinates (circular)
tuv <- matrix(0, nrow = 10, ncol = 2)
alpha <- -360/10
for (i in 1:10){
  alpha <- alpha+360/10
  tuv[i, 1]<- cos(alpha*pi/180)
  tuv[i, 2] <- sin(alpha*pi/180) 
}
fit_vmu2 <- vmu(PVQ40agg, col.coord = tuv)  ## fit 2D circular VMU
fit_vmu2
plot(fit_vmu2, cex = c(1, 0.7))