A gravity-based multidimensional unfolding model for preference data

A new model for analyzing two-way, two-mode preference data is proposed. MultiDimensional Unfolding models (MDU) have been used widely. In these model, the observed preference value is related to the distance between the ideal point and object point only. The market share of each brand is ignored or assumed to be be the same for all objects. The attraction of each object, such as the market share of that object, must be incorporated in the analysis of marketing data. A gravity-based multidimensional unfolding model will be proposed. One specific characteristic of preference data of N subjects is that observed preference values of individuals are often not compatible between individuals. The de-generated configuration problem on applying the non-metric MDU method to a real data set will be caused by the week condition on the data matrix. A linearly constrained nonmetric approach is also proposed to try to rescue from obtaining the de-generated configuration.