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