FITTING A MULTIDIMENSIONAL COMPONENT MODEL TO BINARY DATA.

Abstract

A solution to factoring binary data matrices is proposed by weakening the symmetric-least-squares error function of component analysis to requiring only monotonicity over individuals between item responses and reproduction from the analysis. Two classes of measures of monotonicity are considered: one analogous to regression of the observations on the model (class I) and the other analogous to regression of the model on the observations (class II). Several computing procedures were tried: a gradient-oriented procedure which led to local minima and a refactoring procedure which led to general minima for class II functions but not for class I functions. Solutions for the Class II functions indicated existence of undesirable degenerate results. Suggestions are made for further modified computing procedures for class I functions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1968
Accession Number
AD0677294

Entities

People

  • Raymond Frederick Koopman Jr

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Acquisition
  • Complex Variables
  • Data Acquisition
  • Functions (Mathematics)
  • Mathematical Analysis
  • Observation

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.