One Direction?: Modelling Circular Data in the Social Sciences using the Embedding Approach

Abstract

In the social sciences there are numerous examples of circular data. It occurs in research on the human sense of direction, eye movements or the synchronization of movement or sound. But also when we are interested in the time of day a specific event occurs measurements are on a circular scale. Typical of social science however is that specific circular measurement instruments are used. Examples of these are the political spectrum with its left-right and liberal-conservative axes or the so-called ‘rose of Leary’ from psychology that is used to classify the interactions between individuals. In this dissertation we make use of one specific approach to analyse circular data: the embedding approach. In this approach we assume that the circular variable originates from a projection of a latent variable in bivariate space to the circle. This is advantageous in comparison to other approaches to circular data because we can make use of existing methods for bivariate data, but the interpretation of results can be challenging. We alleviate this disadvantage in interpretation by developing new tools that translate the bivariate results to the circle. Although circular data occurs relatively often in the social sciences, methods that were specifically developed for the use of this data are not used that often. This dissertation therefore has three goals: making methods for circular data available to the applied researcher, testing available methods for circular data and adapting (and extending) those methods to make them fit for use by social scientists.