Visualizing data in social and behavioral sciences: An application of PARAMAP on judicial statistics

Abstract

In this paper, we describe a technique called PARAMAP for the visualization, scaling, and dimensionality reduction of data in the social and behavioral sciences. PARAMAP uses a criterion of maximizing continuity between higher dimensional data and lower dimensional derived data, rather than the distance based criterion used by standard distance based multidimensional scaling (MDS). We introduce PARAMAP using the example of scaling and visualizing the voting patterns of Justices in the US Supreme Court. We use data on the agreement rates between individual Justices in the US Supreme Court and on the percentage swing votes for Justices over time. We use PARAMAP, metric MDS, and nonmetric MDS approaches to create a voting space representation of the Justices in one and two dimensions.We test the results using a metric that measures neighborhood agreement of points between higher and lower dimensional solutions. PARAMAP produces smooth, easily interpretable, solutions, with no clumping together of points. © Springer International Publishing Switzerland 2013.