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Title: Simultaneous analysis in Bayesian multidimensional unfolding with application to party expert surveys Authors:  Kodai Tachibana - University of Tokyo (Japan) [presenting]
Junko Kato - University of Tokyo (Japan)
Kensuke Okada - The University of Tokyo (Japan)
Abstract: Multidimensional unfolding has been applied as a spatial model of choice and judgment in social sciences. However, when estimating the coordinate parameters in an ordinary multidimensional unfolding model with the Markov chain Monte Carlo algorithm, the problem of indeterminacy arises, preventing naive implementation from working properly. This problem occurs because rotation, reflection, and translation of the configuration matrix do not change the likelihood. One of the well-known methods to manage this issue is fixing the required number of coordinates. This approach, however, causes a problem in which it is no longer possible to estimate the uncertainty of the fixed coordinates and a problem in which arbitrary constraints must be made. We propose a different approach using equality constraints in a case in which two datasets are simultaneously analyzed. The proposed constraint allows us to estimate all the relevant parameters under realistic model assumptions. The proposed method is illustrated with expert survey datasets on political parties. Concretely, the spatial representation of the parties and survey items are simultaneously estimated by constraining the party positions to be equal between the two analyzed datasets. The utility and applicability of the proposal are discussed.