Least squares estimation of individual differences in multidimensional scaling

Author:
  • WKWilliam R. Krane
    William R. Krane
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Abstract
It is noted that previous approaches to estimating the parameters of the individual differences model by Bloxom, Horan, Carroll and Chang have involved sequentially fitting the distance component of the model to observed dissimilarity data, then fitting the spatial component to estimated scalar products. Well‐known least squares principles are employed to develop a procedure for estimating all the parameters of the model simultaneously. An objective loss function is established for the problem and the matrix calculus given by McDonald & Swaminathan is applied to obtain sets of equations whose solution provides the least squares estimators of the parameters. Suggestions for the implementation of the proposed method are given. It is shown that a reasonable starting point for an algorithm based on the results of the simultaneous least squares approach may be obtained from the equations derived by Bloxom.