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.

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:

MDS & SurveysBut , 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

MDS & Surveys: 2W2M Data1: 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 program’s limit )

All ideal points/vectors are w.r.t. same Configuration

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,

Kendall’s tau for Likert data) 2W1M for each subgroup

Scale subgroups as “individuals” in INDSCAL.

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., 45:8 (October 1966), pp. 1299-1338.