Browse > Article
http://dx.doi.org/10.5351/KJAS.2018.31.1.067

Multidimensional scaling of categorical data using the partition method  

Shin, Sang Min (Department of Management Information Systems, Dong-A University)
Chun, Sun-Kyung (Department of Statistics, Pusan National University)
Choi, Yong-Seok (Department of Statistics, Pusan National University)
Publication Information
The Korean Journal of Applied Statistics / v.31, no.1, 2018 , pp. 67-75 More about this Journal
Abstract
Multidimensional scaling (MDS) is an exploratory analysis of multivariate data to represent the dissimilarity among objects in the geometric low-dimensional space. However, a general MDS map only shows the information of objects without any information about variables. In this study, we used MDS based on the algorithm of Torgerson (Theory and Methods of Scaling, Wiley, 1958) to visualize some clusters of objects in categorical data. For this, we convert given data into a multiple indicator matrix. Additionally, we added the information of levels for each categorical variable on the MDS map by applying the partition method of Shin et al. (Korean Journal of Applied Statistics, 28, 1171-1180, 2015). Therefore, we can find information on the similarity among objects as well as find associations among categorical variables using the proposed MDS map.
Keywords
pooling the independent cohort data sets; benchmark dose lower limit; linear mixed model; attention deficit hyperactivity disorder; blood lead level;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Choi, Y. S. (2014). Walk in Multidimensional Scaling, Free Academy, Seoul.
2 Cox, T. F. and Cox, M. A. A. (2000). Multidimensional Scaling (2nd ed), Chapman & Hall, London.
3 Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis, Biometrika, 58, 453-467.   DOI
4 Gower, J. C. (1992). Generalized biplots, Biometrika, 79, 475-493.   DOI
5 Gower, J. C. and Hand, D. J. (1996). Biplots, Chapman & Hall, London.
6 Gower, J. C. and Harding, S. A. (1988). Nonlinear biplots, Biometrika, 75, 445-455.   DOI
7 Shin, S. M., Kim, E. S., and Choi, Y. S. (2015). Multidimensional scaling using the pseudo-points based on partition method, Korean Journal of Applied Statistics, 28, 1171-1180.   DOI
8 Torgerson, W. S. (1958). Theory and Methods of Scaling, Wiley, New York.
9 Young, G. and Householder, A. S. (1938). Discussion of a set of points in terms of their mutual distances, Psychometrika, 3, 19-22.   DOI
10 Choi, Y. S. and Shin, S. M. (2013). Understanding of Biplot Analysis using R, Free Academy, Seoul.