optSmacofSymInterval {mdsOpt}

Selecting the optimal multidimensional scaling procedure for interval-valued data

Description

Selecting the optimal multidimensional scaling procedure by varying all combinations of normalization methods, distance measures for interval-valued data, and metric MDS models/

Usage

optSmacofSymInterval(x,dataType="simple",normalizations=NULL,
distances=NULL,mdsmodels=NULL,spline.degrees=c(2),outputCsv="",
outputCsv2="",y=NULL,outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

x

interval-valued data table or matrix or dataset

dataType

Type of symbolic data table passed to function:

'sda' - full symbolicDA format object;

'simple' - three dimensional array with lower and upper bound of intervals in third dimension;

'separate_tables' - lower bound of intervals in x, upper bound of intervals in y;

'rows' - lower and upper bound of intervals in neighbouring rows;

'columns' - lower and upper bound of intervals in neighbouring columns

normalizations

optional, vector of normalization methods that should be used in procedure

distances

optional, vector of distance measures (Hausdorf, Ichino-Yaguchi) that should be used in procedure

mdsmodels

optional, vector of multidimensional models (ratio, interval, mspline) that should be used in procedure

spline.degrees

optional, vector (e.g. 2:4) of spline.degree parameter values that should be used in procedure for mspline model

outputCsv

optional, name of csv file with results

outputCsv2

optional, name of csv (comma as decimal point sign) file with results

y

matrix or dataset with upper bounds of intervals if argument dataType is equal to "separate_tables"

outDec

decimal sign used in returned table

stressDigits

Number of decimal digits for displaying Stress 1 value

HHIDigits

Number of decimal digits for displaying HHI spp value

...

arguments passed to smacofSym, like ndim, itmax, eps and others

Details

Parameter normalizations may be the subset of the following values:

"n1","n2","n3","n3a","n4","n5","n5a","n6","n6a",

"n7","n8","n9","n9a","n10","n11","n12","n12a","n13"

(e.g. normalizations=c("n1","n2","n3","n5","n5a",

"n8","n9","n9a","n11","n12a"))

if normalizations is set to "n0" no normalization is applied

Parameter distances may be the subset of the following values:

"H_q1","H_q2","U_2_q1","U_2_q2" (In following order: Hausdorff distance with q=1, Euclidean Hausdorff distance with q=2, Ichino-Yaguchi distance with q=1; Euclidean Ichino-Yaguchi distance with q=2)

(e.g. distances=c("H_q1","U_2_q1"))

Parameter mdsmodels may be the subset of the following values (metric MDS):

"ratio","interval","mspline" (e.g. c("ratio","interval"))

Value

Data frame ordered by increasing value of Stress-1 fit measure with columns:

Normalization method

normalization method used for p-th multidimensional scaling procedure

MDS model

MDS model used for p-th multidimensional scaling procedure

Spline degree

Additional spline.degree value if mspline model is used for simulation, for other models there is no value in this cell

Distance measure

distance measures for interval-valued data used for p-th multidimensional scaling procedure

STRESS 1

value of Kruskal Stress-1 fit measure for p-th multidimensional scaling procedure

HHI spp

Hirschman-Herfindahl HHI index calculated based on stress per point for p-th multidimensional scaling procedure

Author(s)

Marek Walesiak [e-mail], Andrzej Dudek [e-mail]

Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, Poland

References

Borg, I., Groenen, P.J.F. (2005), Modern Multidimensional Scaling. Theory and Applications, 2nd Edition, Springer Science+Business Media, New York. ISBN: 978-0387-25150-9. Available at: https://link.springer.com/book/10.1007/0-387-28981-X.

Borg, I., Groenen, P.J.F., Mair, P. (2013), Applied Multidimensional Scaling, Springer, Heidelberg, New York, Dordrecht, London. Available at: doi:10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

Herfindahl, O.C. (1950), Concentration in the Steel Industry, Doctoral thesis, Columbia University.

Hirschman, A.O. (1964), The Paternity of an Index, The American Economic Review, Vol. 54, 761-762.

Walesiak, M. (2014), Przegląd formuł normalizacji wartości zmiennych oraz ich własności w statystycznej analizie wielowymiarowej [Data Normalization in Multivariate Data Analysis. An Overview and Properties], Przegląd Statystyczny, tom 61, z. 4, 363-372. Available at: doi:10.5604/01.3001.0016.1740.

Walesiak, M., Dudek, A. (2017), Selecting the Optimal Multidimensional Scaling Procedure for Metric Data with R Environment, STATISTICS IN TRANSITION new series, September, Vol. 18, No. 3, pp. 521-540.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, interval_normalization, dist.Symbolic, smacofSym

Examples

  
 library(mdsOpt)
 library(clusterSim)
 data(data_symbolic_interval_polish_voivodships)
 metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
 metscale<-c("ratio","interval","mspline")
 metdist<-c("H_q1","H_q2","U_2_q1","U_2_q2")
 res<-optSmacofSymInterval(data_symbolic_interval_polish_voivodships,dataType="simple",
 normalizations=metnor,distances=metdist,mdsmodels=metscale,spline.degrees=c(2,3),outDec=".")
 stress<-as.numeric(gsub(",",".",res[,"STRESS 1"],fixed=TRUE))
 hhi<-as.numeric(gsub(",",".",res[,"HHI spp"],fixed=TRUE))
 t<-findOptimalSmacofSym(res)
 cs<-(min(stress)+max(stress))/2 # critical stress
 plot(stress[-t$Nr],hhi[-t$Nr], xlab="Stress-1", ylab="HHI",type="n",font.lab=3)
 text(stress[-t$Nr],hhi[-t$Nr],labels=(1:nrow(res))[-t$Nr])
 abline(v=cs,col="red")
 points(stress[t$Nr],hhi[t$Nr], cex=5,col="red")
 text(stress[t$Nr],hhi[t$Nr],labels=(1:nrow(res))[t$Nr],col="red")
 print(t)