Visualization of Linear Ordering Results for Ordinal Data with Application of Multidimensional Scaling

2017 ◽  
Vol 64 (1) ◽  
pp. 5-20
Author(s):  
Marek Walesiak
Keyword(s):  
Multidimensional Scaling ◽  
Ordinal Data ◽  
Euclidean Distance ◽  
Dimensional Space ◽  
Linear Ordering ◽  
Two Dimensional ◽  
Ideal Object ◽  
Step Procedure

A two-step procedure was proposed to visualization of linear ordering results for ordinal data. In the first step as a result of the application of multidimensional scaling (see Borg, Groenen, 2005; Mair et al., 2016) is to visualize objects in two-dimensional space. In the next step, a linear ordering is carried out with the use of the Euclidean distance from the pattern (ideal) object. The proposed approach expanded the possibilities of interpretation of the results of the linear ordering of set of objects. The article uses the concept of isoquant and path of development (the shortest way connecting ideal and anti-ideal object) proposed by Hellwig (1981). The proposed approach is illustrated by an empirical example with application of script of R environment.

The Concept of Happiness: A Multidimensional Scaling Investigation

1988 ◽  
Vol 27 (2) ◽  
pp. 141-154 ◽  
Author(s):  
Jo Ann Thomas ◽  
William A. Stock
Keyword(s):  
Multidimensional Scaling ◽  
Paired Comparison ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Adult Males ◽  
Comparison Task ◽  
Two Samples ◽  
Age Trends ◽  
Males And Females ◽  
Scaling Analyses

This study investigated the concept of happiness using multidimensional scaling analyses. Two samples were studied. The first contained 100 adult males and females, aged nineteen to ninety ( M = 39.5). The second contained 126 female adults, aged twenty-six to eighty-nine ( M = 61.3), all Catholic nuns. Respondents provided word associates to the words happiness and unhappiness during separate one-minute intervals. Subsequently, the twelve most frequent associates and the word happiness were used in a written paired comparison task of dissimilarities between all possible pairs. In both samples, a two-dimensional space was judged to optimally fit the data. The first dimension was interpreted as a bipolar affective dimension. The second dimension was one-fifth and one-third as salient as the first dimension in the respective samples, and was interpreted as representing personal independence. Two-dimensional spaces of young, middle-aged, and old subsamples of sample one were, in large part, similar to the total space. Three age trends were noted.

A Nonmetric Measure of Euclidean Distance

1994 ◽  
Vol 78 (2) ◽  
pp. 561-562 ◽  
Author(s):  
Frank O'Brien
Keyword(s):  
Simulation Study ◽  
Euclidean Distance ◽  
Large Scale ◽  
Finite Population ◽  
Dimensional Space ◽  
Density Model ◽  
Spatial Density ◽  
Two Dimensional ◽  
Fundamental Properties ◽  
Metric Distance

The results of a large scale simulation study to test the fundamental properties of the author's finite population spatial density model are reported. A conjecture is given relating metric distance to a nonmetric estimate in two-dimensional space.

A Least Squares Fit for Comparison of Configurations of Points in Two-Dimensional Space

1971 ◽  
Vol 28 (3) ◽  
pp. 999-1002
Author(s):  
Joseph Levin
Keyword(s):  
Multidimensional Scaling ◽  
Least Squares ◽  
Dimensional Space ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Coordinate Systems ◽  
Linear Transformations ◽  
Least Squares Fit ◽  
Geometric Space

Multidimensional scaling techniques map a set of objects into geometric space, usually Euclidean. As the solutions are not unique, and linear transformations are admissible operations, two solutions for a given set of objects are not comparable owing to differences of the coordinate systems. A Transformation of coordinates to obtain a least squares fit of two configurations is derived for the two-dimensional case.

scholarly journals Mental Representations of Values and Behaviors

2021 ◽  
pp. 089020702110343
Author(s):  
Gabriel Lins De Holanda Coelho ◽  
Paul H. P. Hanel ◽  
Mark K. Johansen ◽  
Gregory R. Maio
Keyword(s):  
Multidimensional Scaling ◽  
Spatial Representation ◽  
Social Values ◽  
Mental Representations ◽  
Dimensional Space ◽  
Spatial Representations ◽  
Two Dimensional ◽  
New Approach ◽  
Approach To Learning ◽  
Direct Assessment

The present research provides the first direct assessment of the fit of diverse behaviors to putatively related personal and social values from Schwartz’s theory. Across three studies, we examined spatial representations of value-related behaviors that were explicitly derived from people’s mental representations of the values. Participants were asked how similar the behaviors were to each other and various values, and these judgments were used to specify multidimensional scaling solutions. The results indicated that the spatial representation of the behaviors was consistent with the two-dimensional space described in Schwartz’s model of values, although several deviations occurred. For example, self-enhancement behaviors were widely spread, indicating more variation in the way individuals interpret these behaviors, which are often associated with other value types. These data provide evidence that a range of behaviors can at least partly be reduced to underlying motivations expressed by values. Furthermore, our findings indicate that behaviors are often expressed by several values, which might help to explain why value–behavior associations in previous studies were weak. Finally, they illustrate a new approach to learning which behaviors might relate to multiple values.

Seeded Growth of Single-Crystal Two-Dimensional Covalent Organic Frameworks

2017 ◽  
Author(s):  
Austin M. Evans ◽  
Lucas R. Parent ◽  
Nathan C. Flanders ◽  
Ryan P. Bisbey ◽  
Edon Vitaku ◽  
...  
Keyword(s):  
Molecular Transport ◽  
Controlled Synthesis ◽  
Two Dimensional ◽  
Covalent Organic Frameworks ◽  
Seeded Growth ◽  
Covalent Bonds ◽  
Crystalline Materials ◽  
Step Procedure ◽  
Structures And Properties ◽  
2D Polymer

<div> <div> <div> <p>Polymerizing monomers into periodic two-dimensional (2D) networks provides structurally precise, atomically thin macromolecular sheets linked by robust, covalent bonds. These materials exhibit desirable mechanical, optoelectrotronic, and molecular transport properties derived from their designed structure and permanent porosity. 2D covalent organic frameworks (COFs) offer broad monomer scope, but are generally isolated as polycrystalline, insoluble powders with limited processability. Here we overcome this limitation by controlling 2D COF formation using a two- step procedure. In the first step, 2D COF nanoparticle seeds are prepared with approximate diameters of 30 nm. Next, monomers are slowly added to suppress new nucleation while promoting epitaxial growth on the existing seeds to sizes of several microns. The resulting COF nanoparticles are of exceptional and unprecedented quality, isolated as single crystalline materials with micron-scale domain sizes. These findings advance the controlled synthesis of 2D layered COFs and will enable a broad exploration of synthetic 2D polymer structures and properties. </p> </div> </div> </div>

Seeded Growth of Single-Crystal Two-Dimensional Covalent Organic Frameworks

2017 ◽  
Author(s):  
Austin M. Evans ◽  
Lucas R. Parent ◽  
Nathan C. Flanders ◽  
Ryan P. Bisbey ◽  
Edon Vitaku ◽  
...  
Keyword(s):  
Molecular Transport ◽  
Controlled Synthesis ◽  
Two Dimensional ◽  
Covalent Organic Frameworks ◽  
Seeded Growth ◽  
Covalent Bonds ◽  
Crystalline Materials ◽  
Step Procedure ◽  
Structures And Properties ◽  
2D Polymer

<div> <div> <div> <p>Polymerizing monomers into periodic two-dimensional (2D) networks provides structurally precise, atomically thin macromolecular sheets linked by robust, covalent bonds. These materials exhibit desirable mechanical, optoelectrotronic, and molecular transport properties derived from their designed structure and permanent porosity. 2D covalent organic frameworks (COFs) offer broad monomer scope, but are generally isolated as polycrystalline, insoluble powders with limited processability. Here we overcome this limitation by controlling 2D COF formation using a two- step procedure. In the first step, 2D COF nanoparticle seeds are prepared with approximate diameters of 30 nm. Next, monomers are slowly added to suppress new nucleation while promoting epitaxial growth on the existing seeds to sizes of several microns. The resulting COF nanoparticles are of exceptional and unprecedented quality, isolated as single crystalline materials with micron-scale domain sizes. These findings advance the controlled synthesis of 2D layered COFs and will enable a broad exploration of synthetic 2D polymer structures and properties. </p> </div> </div> </div>

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

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