Module 1: INTRODUCTION TO MULTIDIMENSIONAL SCALING

The purpose of the first module is to give you the means of bringing order to the often confusing “MDS world” with its wide range of models and programs. To do this, I use the three components: DATA - FUNCTION - MODEL to give a common framework to subsequent work. 

DATA: You have to understand the WAY (array dimensionality) and the MODE (number of distinct sets) of input data matrices , and be familiar with Symmetric and Asymmetric; Upper-, Lower-triangular and Full matrices. The contents of the matrix are Direct and Aggregate measures of dis/similarity (see ch.2 of TUG)

FUNCTION: The level of measurement for the data, and the permissible transformations implied by ordinal and interval data; regular and irregular monotonic transformations are of special importance.

MODEL: The representation of the data in the solution. The [Euclidean] distance model is crucial, but be aware of the City Block model. The factor/scalar-products model will soon feature, too.

The BASIC MDS MODEL now becomes the focus: Analysis of a 2W1M (LT) matrix of dis/similarities by the Euclidean Distance model, using an ordinal/monotonic transformation. Given simply the rank order of a set of “distances” (data) it generates the map (solution) which produced them. It works (European capitals.

PROGRAMS: - Main recommended package is SPSS10's PROXSCAL. (ALSCAL has problems and should be used with caution, if at all). 

- The main Library of MDS programs used is: NewMDSX (Windows, or MS-DOS). Basic model = MINISSA 

- For interactive work, and ensuring a global minimum (and for fun!), use PERMAP with MDS Type = Ordinal

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