Constrained Multidimensional Scaling in N Spaces

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Abstract
A gradient method is used to obtain least squares estimates of parameters of the m-dimensional euclidean model simultaneously in N spaces, given the observation of all pairwise distances of n stimuli for each space. The procedure can estimate an additive constant as well as stimulus projections and the metric of the reference axes of the configuration in each space. Each parameter in the model can be fixed to equal some a priori value, constrained to be equal to any other parameter, or free to take on any value in the parameter space. Two applications of the procedure are described.