findOptimalSmacofSym {mdsOpt}

Selecting the optimal multidimensional scaling (MDS) procedure

Description

Selecting the optimal multidimensional scaling procedure - metric MDS (by varying all combinations of normalization methods, distance measures, and metric MDS models) and nonmetric MDS (by varying all combinations of normalization methods and distance measures)

Usage

findOptimalSmacofSym(table,
critical_stress=(max(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE)))+
min(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE))))/2,
critical_HHI=NA)

Arguments

table

result from optSmacofSym_nMDS or optSmacofSym_mMDS. Data frame ordered by increasing value of Stress-1 fit measure or HHI index with columns:

Normalization method

Distance measure

MDS model

Spline degree

STRESS 1

HHI spp

critical_stress

threshold value of Kruskal's Stress-1 fit measure. Default - mid-range of Kruskal's Stress-1 fit measures calculated for all MDS procedures

critical_HHI

threshold value of Hirschman-Herfindahl HHI index. Only one parameter critical_stress or critical_HHI can be set, and the function finds the optimal value among the procedures for which the selected measure is lower or equal treshold value

Value

Nr

number of row in table with optimal multidimensional scaling procedure

Normalization_method

normalization method used for optimal multidimensional scaling procedure

MDS_model

MDS model used for optimal multidimensional scaling procedure

Spline_degree

Additional spline.degree value for optimal procedure, if mspline model is used for simulation. For other models there is no value for this field

Distance_measure

distance measure used for optimal multidimensional scaling procedure

STRESS_1

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

HHI_spp

Hirschman-Herfindahl HHI index, calculated based on stress per point, for optimal 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<-c("ratio","interval")
  metdist<-c("euclidean","manhattan","maximum","seuclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_mMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale,outDec=".")
  print(findOptimalSmacofSym(res))