Module 6: EXTENSIONS OF BASIC MODEL: TWO-WAY TWO-MODE (RECTANGULAR) DATA

          

The Basic (non-metric ) model has been extended in a variety of ways - different data, functions, models. In the time available, we can only look at some more frequently used extensions. First - extending the basic 2W1M model to the linear/metric transformation (akin to, but supplanting “classic MDS”), and then to two models for analysis of the Two-way, TWO-MODE data (so-called “rectangular data”), the vector model aka Multidimensional Preference, simple Correspondence Analysis, and the distance model, aka Multidimensional Unfolding.

The key concepts are:

- SVD (Singular Value Decomposition) for both 2W1M and 2W2M Vector/CA models , a variant of the Eigen structure of a matrix;

- Row-conditional data (and col.-cond) which 2W2M data are, and which means Stress(2) has to be used;

- Biplots & Inter-set comparability (whether or not you can compare across the row/column element element-sets in interpreting Biplot data).

The material in this module is covered primarily in TUG, chapters 5 & 6 (which read now), and the site also gives a paper (by u-know-who) on the important Delbeke data-set analysed by these models.

The programs are:

- NewMDSX’s 

MRSCAL for metric scaling of the basic model, and 

MINI-RSA for non-metric unfolding/distance model ; 

MDPREF for metric vector model;

CORRESP for simple Correspondence Analysis

- SPSS ALSCAL (yes, I know ....) For rectangular data with the ordinal and linear options.

You should run these programs with test data to become familiar with what they do;  try the Delbeke data first.

Downloads

All files are in Acrobat PDF format: Double click on the file title to read on line, or use your right mouse button to "Save target as" to save the file to your disk.

Basic Reading:Chapter 6 of "The User's Guide to MDS"
Chapter 10 of "Key Texts in MDS"
Lecture Notes:2W2M Data
Correspondence Analysis
Delebeke/Bollen Data
MDPREF Note
Rmnyca2d.bmp
Delebeke 2D RSA and MDPREF
 MDS Surveys and Large Data Sets