Some generalized methods of optimal scaling and their asymptotic theories: The case of multiple responses-multiple factors
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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.
KeywordsEigenvalue Problem Response Item Asymptotic Property Determinantal Equation Sample Criterion
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- Tanaka, Y. (1978). Some generalized methods of optimal scaling and their asymptotic theories: The case of single response-multiple factors, to appear. Also see, Tanaka, Y. and Asano, C. (1978),Research Report No. 77, Research Institute of Fundamental Information Science, Kyushu Univ.Google Scholar