An Introduction to MDS
The fundamental idea of scaling is to produce range of scores that
have meaning either with respect to each other's values or to some
arbitrary or absolute value set or accepted by the scale.
(Schiffman, Reynolds, & Young, 1981)
*A scale can be nominal, ordinal, interval, or ratio in nature
*Provides rules for measurement
*Allows for easy interpretation
*Generally subdivided into two classes:
1) Undimensional scales - measure variation with respect to one
attribute (e.g. population size, social ranks, degree of urbanization, color, hue, etc...)
2) Multidimensional scaling (MDS) - aims at developing
procedures that will assign sets of numbers of various quantities of the
attributes among the phenomena being scaled.
Multidimensional Scaling (MDS)
MDS refers to a family of data analysis methods which portray data's
structure in a spatial fashion easily assimilated by the relatively
untrained human eye." (Young, 1985)
*Data is displayed
at points within a 2 (or higher) dimensional plane to
capture it's full complexity
*Wide variety of models and methods exist acoss many diverse fields
(e.g. psychology, marketing, sociology, physics, political science, speech-language pathology)
*Specific classifications of MDS include:
Nonmetric MDS - Qualitative
Metric MDS - Quantitative
*MDS is further classified into:
Classical MDS - 1 matrix, unweighed model
Replicated MDS - several matrices, unweighted model
Weighted MDS - several matrices, weighted model.
Therefore, the purpose of MDS is to systematize and compress large amounts of data in areas where organizing concepts and underrlying dimensions are not well developed. (Kempster, Kistler, & Hillenbrano, 1991)
purpose that design techniques share (despite diversity) is
1) To obtain a method for observing whatever pattern or structure may
lie hidden in a matrix of emperical data.
2) To representing the structure in a form that is more accessible
to the human eye (i.e. geometrical model or picture).
*An ideal multidimensional scaling experiment involves gathering four
types of data:
a) Similarity judgements among all pairs of stimuli
b) Ratings of stimuli on descriptors such as adjectives
c) Objective measures
d) Information about subjects and explanation
A model is chosen to best capture the structure inherent in the data
(Carroll & Arabie, 1980)
Data are represented as points on a spatial map.
*Data judged to be experimentally similar to one another are represented
as points close to eachother.
*Dissimilar data are represented as points distant from one another.
Interpretation: significant features of the data can be revealed in
geometrical relations among the points. (Davison, 1983)
"Dimensions resulting from a MDS analysis are initially 'nameless.'
The procedure does not suggest labels and must be interpreted according
to some theoretical framework." (Gelfer, 1993)
* Depends on the number and nature of stimuli:
a) The order of stimulus presentation
b) Selection of stimulation set
c) Selection of subjects
d) Setting subjects to understand what they need to do
*MINISSA *POLYCON *KYST *INDSCAL *ALSCAI *MULTISCALE
to learn more about computer programs for MDS.
First you jump off the cliff
and you build your wings on the way down.
Cummins - 2001