  Multidimensional unfolding methods are widely used for visualizing item
response data. Such methods project respondents and items simultaneously onto a
low-dimensional Euclidian space, in which respondents and items are represented
by ideal points, with person-person, item-item, and person-item similarities
being captured by the Euclidian distances between the points. In this paper, we
study the visualization of multidimensional unfolding from a statistical
perspective. We cast multidimensional unfolding into an estimation problem,
where the respondent and item ideal points are treated as parameters to be
estimated. An estimator is then proposed for the simultaneous estimation of
these parameters. Asymptotic theory is provided for the recovery of the ideal
points, shedding lights on the validity of model-based visualization. An
alternating projected gradient descent algorithm is proposed for the parameter
estimation. We provide two illustrative examples, one on users' movie rating
and the other on senate roll call voting.
