optSmacofSym_nMDS {mdsOpt}

Selecting the optimal multidimensional scaling procedure - nonmetric MDS

Description

Selecting the optimal multidimensional scaling procedure by varying all combinations of normalization methods and distance measures

Usage

optSmacofSym_nMDS(x,normalizations=NULL,distances=NULL,
mdsmodels=c("ordinal"),weights=NULL,
outputCsv="",outputCsv2="",outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

x

matrix or dataset

normalizations

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

distances

optional, vector of distance measures (manhattan, Euclidean, Chebyshew, squared Euclidean, GDM1) that should be used in procedure

mdsmodels

"ordinal" (nonmetric MDS)

weights

optional, variable weights used in distance calculation. Each weight takes value from interval [0; 1] and sum of weights equals one

outputCsv

optional, name of csv file with results

outputCsv2

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

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

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:

"euclidean", "manhattan","maximum","seuclidean","GDM1"

(e.g. distances=c("euclidean","manhattan"))

Parameter mdsmodels "ordinal" MDS model (nonmetric MDS)

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

"ordinal" MDS model (nonmetric MDS) for p-th multidimensional scaling procedure

Distance measure

distance measure 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. (2016a), Wybór grup metod normalizacji wartości zmiennych w skalowaniu wielowymiarowym [The Choice of Groups of Variable Normalization Methods in Multidimensional Scaling], Przegląd Statystyczny, tom 63, z. 1, 7-18. Available at: doi:10.5604/01.3001.0014.1145.

Walesiak, M. (2016b), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: doi:10.15611/ekt.2016.2.01.

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, dist.GDM, dist, smacofSym

Examples

  
  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-"ordinal"
  metdist<-c("euclidean","manhattan","maximum","seuclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_nMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale)
  stress<-as.numeric(gsub(",",".",res[,"STRESS 1"],fixed=TRUE))
  hhi<-as.numeric(gsub(",",".",res[,"HHI spp"],fixed=TRUE))
  cs<-(min(stress)+max(stress))/2 # critical stress
  t<-findOptimalSmacofSym(res,critical_stress=cs)
  print(t)
  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")