Homogeneity analysis with k sets of variables: An alternating least squares method with optimal scaling features

Eeke van der Burg, Jan de Leeuw, R. Verdegaal

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Abstract

Homogeneity analysis, or multiple correspondence analysis, is usually applied to k separate variables. In this paper, it is applied to sets of variables by using sums within sets. The resulting technique is referred to as OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: (1) nominal; (2) ordinal; and (3) numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and non-linear multivariate analysis techniques are shown to be special cases of OVERALS. Disadvantages of the OVERALS method include the possibility of local minima in some complicated special cases, a lack of information on the stability of results, and its inability to handle incomplete data matrices. Means of dealing with some of these problems are suggested (i.e., an alternating least squares algorithm to solve the minimization problem). An application of the method to data from an epidemiological survey is provided.
Original languageEnglish
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages57
Publication statusPublished - 1986

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.86-5

Keywords

  • Least Squares Statistics
  • Linear Programming
  • Surveys
  • Computer Software
  • Multivariate Analysis
  • Algorithms

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