Abstract
A metric multidimensional unfolding procedure is proposed to represent the rows (individuals) and columns (items) of a proximity data matrix as the points in a low-dimensional space. The procedure is based on a random effect model which allows us to avoid the problem of incidental parameters. In the model, the individual points are regarded as normally-distributed random variables, while the item points are regarded as fixed parameters. The probability density of the proximity data is derived from the assumption that the true proximity is a linear function of the distance from the individual point to the item point and the observed proximity is perturbed by the normally-distributed error. The marginal likelihood obtained by integrating out the random individual points is maximized using the EM algorithm with a generalized SMACOF algorithm. The proposed procedure is evaluated with a simulation study and is applied to a preference rating data.
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