MDS Surveys

1
MDS Surveys Large Data Sets

• MDS developed in context of Psychology.Typically
• small numbers of individuals
• modest number of objects
• For 2W1M data, there is usually no problem
• Aggregate over individuals for dissimilarity
  measures between objects.
• If needs be, program sizes can be increased
• The restrictions arise from original programming
  languages
• Which had no provision for dynamic allocation of
  arrays.
• Tho for Q analysis with large N, there may be a
  problem.

2
MDS Surveys Large Data Sets

• Large Number Problems usually arise in the case
  of large numbers of individuals
• In 2W2M (where 1st mode is often individuals)
• In 3W data(where one mode is often individuals).
• Before you proceed THINK
• Do you REALLY wish to parameterize a large number
  ( even thousands) of individuals?
• AND, if you do, how will you actually analyse
  them, or build them into your model?
• But if you DO have large numbers, then STRATEGIES
  you might adopt include the following

3
MDS Surveys

• But , if you think you have problems
• Kruskal Hart (1966)Geometric Interpretation of
  Diagnostic Data From a Digital Machine
• 30,000 computer malfunctions! (co-occurrences)
• And in early days of small computer memories!
• So, how did he do it?
• Overlapping random samples of objects
• Each scaled, using fix co-ordinates
• Mapped into 6-D space!
• Which provided diagnostic key for future failures

4
MDS Surveys 2W2M Data

• 1 The External Fix Pour in batches
  Strategy
• Scale Group/stimulus Space
• Possibly using overlapping samples and Procrustes
• Do an External analysis with 2W2M data, using
  PREFMAP 3 and/or 4
• FIX Group Space Configuration
• Then Input batches of individuals data
• ( up to programs limit )
• All ideal points/vectors are w.r.t. same
  Configuration

5
MDS Surveys (3W data)

• 2 MAKE SUB-GROUPS YOUR UNIT
• Represent pseudo-individuals , i.e.
• Subgroups defined either by combination of a
  priori characteristics
• OR defined by previously-detected a posteriori
  Clusters
• THEN aggregate (average) within each sub-group
• Calculate dissimilarity measure (eg G-K gamma,
  Kendalls tau for Likert data) 2W1M for each
  subgroup
• Scale subgroups as individuals in INDSCAL.

6
MDS, Surveys, Large Nos.References

• Coxon, A.P.M. Jones, C.L. (1977) 'Applications
  of multidimensional scaling techniques in the
  analysis of survey data' in C.A. O'Muircheartaigh
  and C. Payne, The Analysis of Survey Data
  Exploring Data Structures London, Wiley.
• Kruskal, J.B. and R. E. Hart A Geometric
  Interpretation of Diagnostic Data From a Digital
  Machine Based on a Study of the Morris, Illinois
  Electronic Central Office, Bell Sys. Tech. J.,
  458 (October 1966), pp. 1299-1338.