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MDS Surveys & Large Data Sets

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.

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MDS Surveys & Large Data Sets

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  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 program’s 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, Kendall’s tau for Likert data) 2W1M for eachsubgroup • 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., 45:8 (October 1966), pp. 1299-1338.

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