VIPSCAL: A combined vector ideal point model for preference data

In this paper, we propose a new model that combines the vector model and the ideal point model of unfolding. An algorithm is developed, called VIPSCAL, that minimizes the combined loss both for ordinal and interval transformations. As such, mixed representations including both vectors and ideal points can be obtained but the algorithm also allows for the unmixed cases, giving either a complete ideal pointanalysis or a complete vector analysis. On the basis of previous research, the mixed representations were expected to be nondegenerate. However, degenerate solutions still occurred as the common belief that distant ideal points can be represented by vectors does not hold true. The occurrence of these distant ideal points was solved by adding certain length and orthogonality restrictions on the configuration. The restrictions can be used both for the mixed and unmixed cases in several ways such that a number of different models can be fitted by VIPSCAL.