Multi - What?

             An Introduction to MDS


                         * Definitions            * Purpose          *Computer Programs

                 * Procedure            *Benefits           * Drawbacks


    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.

A problem encountered by researchers in many disciplines including our field is how to measure and understand the relationships between objects when the underlying dimensions are not known.

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)

        *The unifying 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).


Data are gathered
        *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)

        Time Requirement:
        * 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

Benefits of MDS
Promotes understanding of complex data
Can be applied to very wide range of types of data
Makes it possible to differentiate among instances that may be lumped
    together in given class of things (e.g. degrees of warmth)
Allows systematic manipulation of the scaled items in conformance with
    concepts and theories of logic and mathematics
Can show relative positions rather than just difference
Provides space that reveals dimensions relevant to subjects
Prior knowledge of the stimuli to be scaled is not required
Low in experimental contamination

Drawbacks of MDS
Problem of knowing if a method is appropriate to use
Problem of interpretation - may be using an appropriate method but may not
    provide right (real) insight into phenomenon under study
Procedure of finding interpretable axes becomes more difficult with increased
    number of dimensions
Can be time consuming
MDS may serve as a guide but never as a substitute for careful understanding
    or creative thought!

Computer Programs

          *MINISSA     *POLYCON     *KYST      *INDSCAL     *ALSCAI      *MULTISCALE

Click here:     to learn more about computer programs for MDS.



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                                      First you jump off the cliff
                    and you build your wings on the way down.
                                                     Ray Bradbury

                                                                                    Cummins - 2001