Bayesian models for circular data using the projected normal distribution

Jolien’s PhD project focuses on the embedding approach to circular data, specifically on models employing the projected normal (PN) distribution. The embedding approach is very flexible and within the approach many complex models for circular data exist. It also is a so-called consensus model which means that the circular location and spread are modeled simultaneously. Interpretation of the parameter estimates from these models however is challenging. Sub-projects are:

• PN regression models.
  • In three papers the focus has been on Bayesian PN regression models. First, the performance of two MCMC algorithms for estimating PN regression models has been investigated. In this project, we have also analysed data from an interpersonal circumplex using the PN regression model. In a second paper, several measures were developed that make the interpretation of regression effects on the circle easier. In a third paper, we introduce and compare several tools that can be used to distinguish between accuracy and location effects in a PN regression model.
• PN mixed-effects models.
  • In this paper we focus on modelling a Bayesian PN mixed-effects model to longitudinal teacher behavior data from an interpersonal circumplex. We focus on how a circular model enriches our understanding of this type of data and we introduce new tools to make the interpretation of effects from a PN mixed-effects model easier.
• An R-package for PN regression and mixed-effects models.
• A tutorial on circular data in psychology.
• Cylindrical models for circumplex data.
  • In this paper we extend four models for cylindrical data and fit them to circumplex data.