## A generalized method of optimal scaling for partially ordered categoriesKyushu University, Research Institute of Fundamental Information Science, 1977 - Mathematics - 25 pages |

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3j Notice a(directed applied arbitrary order restrictions arbitrary testable hypothesis Bradley canonical correlation coefficient Chooichiro Asano connected graph contain any circuit correlation ratio Criteria for optimal criterion in Hayashi's Cycle denote the number edge equality restrictions corresponding exists no equality expressed by Fig factor item formulation Fukuoka Fundamental Information Science Hayashi's second method initial values Katti and Coons KYUSHU UNIVERSITY linear programming linearly dependent M(Tk matrix T c+m)xr Method of Optimal method of quantification Nishisato and Arri optimal scaling optimal values optimization problem order relations order restrictions tj Partially Ordered Categories problem of optimal procedure converges rapidly reduced gradient method response item restrictions are expressed result shown rk-l row vectors satisfying Scaling for Partially scaling under order separable programming set of order shown in Table Solution obtained solve squared partial submatrix subset tions tj i tj transformation matrix transformed variables variation due Wolfe's reduced gradient yields the result Yutaka Tanaka