Some generalized methods of optimal scaling and their asymptotic theories: The case of multiple responses-multiple factors

  • Yutaka Tanaka


Seven generalized criteria are proposed with the corresponding formulations for optimal scaling of multiple responses. Then, on the basis of a natural probabilistic model, the asymptotic theories are derived concerning the test statistics on factor-response relationships as well as the distributions of sample criteria (eigenvalues of the determinantal equation) and optimal scores (eigenvectors) by means of socalled δ-method. A numerical example is provided for illustrations.


Eigenvalue Problem Response Item Asymptotic Property Determinantal Equation Sample Criterion 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1978

Authors and Affiliations

  • Yutaka Tanaka
    • 1
  1. 1.Takeda Chemical Industries, Ltd.OsakaJapan

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