# Multidimensional Scaling

Sean Eom (Southeast Missouri State University, USA)
DOI: 10.4018/978-1-59904-738-6.ch010

## Abstract

This chapter discusses multidimensional scaling (MDS) procedures. MDS is a class of multivariate statistical techniques/procedures to produce two or three dimensional pictures of data (geometric configuration of points) using proximities among any kind of objects as input. Three SAS procedures (MDS, PLOT, and G3D) are necessary to convert the author cocitation frequency matrix to two or three dimensional pictures of data. The distance matrix produced earlier by using xmacro.sas and distnew.sas programs should be converted to a coordinate matrix, to produce twodimensional plots, and annotated three-dimensional scatter diagrams. This chapter also discusses how to label data points on a plot. The annotate facility in the SAS system produces figures with the name of the author on each data point. The PROC MDS procedure includes many of the features of the ALSCAL procedure.
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## The Mds Procedure

Multidimensional scaling is a multivariate statistical analysis tool for examining proximity data among any kind of object. Proximity data consist of one or more square symmetric or asymmetric matrices of similarities or dissimilarities between objects or stimuli (Joseph B. Kruskal & Wish, 1978, pp. 7-11). The MDS outputs consist of a spatial representation of data which shows underlying relationships on a two or three dimensional map. The MDS map helps visualize relationships more clearly using the ratio of distances on a map to corresponding data values such as a map of a country showing cities. The magnitude of the number indicates how similar/dissimilar two objects are.

### Similarity/Proximity Measures

How should the inter-object similarity be measured? Numerous ways of measuring inter-object similarity exist. The non-metric data measures the distance by directly ranking the objects from most preferred to least preferred (preference data) and using the pairwise comparison (similarity data) to determine which items are most similar/dissimilar to each other (all pairs of these objects can be compared).

To measure proximities among authors, the correlations among authors are used most frequently. Correlations are used as proximities by MDS procedures (Joseph B. Kruskal & Wish, 1978). The author cocitation frequency is metric data. As in the PROC Cluster procedure, the cocitation frequency matrix must be converted into a ordinary Euclidian distance data matrix using METHOD= DCORR, This method transformed correlations to Euclidean distance using square root of (1-CORR). Figure 2 shows MDS SAS procedure statements.

Figure 2.

Proc MDS with an imported data set from an Excel file

### Proc MDS Statement

The MDS procedure produces only the iteration history. The procedure does not produce any graphical outputs. It is necessary for ACA analysts to specify several options. The minimum essential options include data=, dimension=, and out= .

The PROC MDS statement is required. All other statements are optional.

`PROC MDS < options > ;VAR variables ;INVAR variables ;ID|OBJECT variable ;MATRIX|SUBJECT variable ;WEIGHT variables ;BY variables ;`

Since the MDS procedure produces only the printed iteration history, specifying options are necessary to produce other results listed below.

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