Selecting the Optimal Multidimensional Scaling Procedure for Metric Data With R Environment

Walesiak, Marek; Dudek, Andrzej

doi:10.21307/stattrans-2016-084

Cited by 22 publications

(25 citation statements)

References 16 publications

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“…In the classic-to-classic approach, an optimal scaling procedure was selected after testing combinations of 6 normalization methods (n1, n2, n3, n5, n5a, n12a see Walesiak, Dudek 2018a), 4 distance measures (Manhattan, Euclidean, Chebyshev, Squared Euclidean, GDM1) and 4 MDS models (ratio, interval, mspline of second and third degree -Borg, Groenen 2005, p. 202)altogether 120 MDS procedures. As a result of applying the optSmacofSym_mMDS function from the mdsOpt R package (see Walesiak, Dudek 2017;2018b), the optimal MDS procedure was selected. The procedure uses the normalization method n2 (positional standardization), the mspline 2 scaling model (polynomial of second degree) and the GDM1 distance.…”

Section: Results Of the Empirical Studymentioning

confidence: 99%

A Comparative Analysis of Economic Efficiency of Medium-Sized Manufacturing Enterprises in Districts of Wielkopolska Province Using the Hybrid Approach With Metric and Interval-Valued Data

Dehnel

Walesiak

2019

Statistics in Transition New Series

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The article describes a hybrid approach to evaluating economic efficiency of medium-sized manufacturing enterprises (employing from 50 to 249 people) in districts of Wielkopolska province, using metric and interval-valued data. The hybrid approach combines multidimensional scaling with linear ordering. In the first step, multidimensional scaling is applied to obtain a visual representation of objects in a two-dimensional space. In the next step, a set of objects is ordered linearly based on the distance from the pattern (ideal) object. This approach provides new possibilities for interpreting linearly ordered results of a set of objects. Interval-valued variables characterise the objects of interests more accurately than metric data do. Metric data are atomic, i.e. an observation of each variable is expressed as a single real number. In contrast, an observation of each interval-valued variable is expressed as an interval. The analysis was based on data prepared in a two-stage process. First, a data set of observations was obtained for metric variables describing economic efficiency of medium-sized manufacturing enterprises. These unit-level data were aggregated at district level (LAU 1) and turned into two types of data: metric and interval-valued data. In the analysis of interval-valued data, two approaches are used: symbolic-to-classic, symbolic-to-symbolic. The article describes a comparative analysis of results of the assessment of economic efficiency based on metric and interval-valued data (the results of two approaches). The calculations were made with scripts prepared in the R environment.

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Section: Results Of the Empirical Studymentioning

confidence: 99%

A Comparative Analysis of Economic Efficiency of Medium-Sized Manufacturing Enterprises in Districts of Wielkopolska Province Using the Hybrid Approach With Metric and Interval-Valued Data

Dehnel

Walesiak

2019

Statistics in Transition New Series

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“…matrix ] [ ij x , c) when calculating distances between objects equal weights were adopted for sub-criteria (domains), but differentiated for the variables presented in Table 1. The article uses the mdsOpt package of the R program [Walesiak, Dudek 2017b] allowing the choice of optimal multidimensional scaling procedure in accordance with the procedure presented in the study [Walesiak, Dudek 2017c].…”

Section: Empirical Research Resultsmentioning

confidence: 99%

“…The solution allowing the choice of an optimal multidimensional scaling procedure was used in the article due to the application of the variables normalization method, distance measure and scaling models, according to the procedure presented in [Walesiak, Dudek 2017c]. The procedure available in the mdsOpt package [Walesiak, Dudek 2017b] of R program applies the smacofSym function of the smacof package [Mair et al 2017].…”

Section: Methodsmentioning

confidence: 99%

The Application of Multidimensional Scaling to Measure and Assess Changes in the Level of Social Cohesion of the Lower Silesia Region in the Period 2005-2015

Walesiak¹

2017

Ekonometria

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Summary: Social cohesion is the ability of territorial communities to ensure the welfare of all its members, to reduce social stratification and avoid polarization (EU/EC/CE 2004, p. 3). The assessment of social cohesion of the Lower Silesia region in the cross-section of counties in the period 2005-2015, was performed based on the variables from the following areas: income and economic activity of the population, living conditions of the population and the availability of services and public space. Multidimensional scaling combined with linear ordering and Theil decomposition were applied to measure and assess changes in the level of social cohesion of the Lower Silesia region in the cross-section of counties in the period 2005-2015. The level of social cohesion of all the counties (although in varying degrees) was increased and the degree of differentiation of social cohesion was slightly decreased during this period. The calculations were made with scripts prepared in R environment.Keywords: social cohesion, multidimensional scaling, linear ordering, GDM1 distance, Theil decomposition, R program. Słowa kluczowe: spójność społeczna, skalowanie wielowymiarowe, porządkowanie liniowe, odległość GDM1, dekompozycja Theila, program R.

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“…To ensure an optimal procedure of multidimensional scaling, we selected methods of normalising variable values, distance measures, and scaling models according to the procedures (for metric and interval-valued data) available in the mdsOpt package (Walesiak & Dudek 2018b), which employ the smacofSym function from the smacof package (Mair et al 2018). More details about the selection of the optimal procedure of multidimensional scaling can be found in Walesiak & Dudek (2017).…”

Section: Methodsmentioning

confidence: 99%

Comparative Analysis of the Ordering of Polish Provinces in Terms of Social Cohesion

Dehnel¹,

Walesiak²,

Obrębalski³

2019

AOC

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The article describes an assessment of the social cohesion of Polish provinces. The assessment was based on classical metric and interval-valued data using a hybrid approach combining multidimensional scaling with linear ordering. In the first step, after applying multidimensional scaling, the objects of interest were represented in a two-dimensional space. In the second step, the objects were linearly ordered based on the Euclidean distance from the pattern object. Interval-valued variables characterize the objects of interests more accurately than do metric data. Classic data are of an atomic nature, i.e. an observation of each variable is expressed as a single real number. By contrast, an observation of each interval-valued variable is expressed as an interval. Interval-valued data were derived by aggregating classic metric data on social cohesion at the level of districts to the province level. The article describes a comparative analysis of the results of an assessment of the social cohesion of Polish provinces based on classical metric data and interval-valued data.

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Selecting the Optimal Multidimensional Scaling Procedure for Metric Data With R Environment

Cited by 22 publications

References 16 publications

A Comparative Analysis of Economic Efficiency of Medium-Sized Manufacturing Enterprises in Districts of Wielkopolska Province Using the Hybrid Approach With Metric and Interval-Valued Data

A Comparative Analysis of Economic Efficiency of Medium-Sized Manufacturing Enterprises in Districts of Wielkopolska Province Using the Hybrid Approach With Metric and Interval-Valued Data

The Application of Multidimensional Scaling to Measure and Assess Changes in the Level of Social Cohesion of the Lower Silesia Region in the Period 2005-2015

Comparative Analysis of the Ordering of Polish Provinces in Terms of Social Cohesion

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