Circular Data in the Social Sciences

During my masters and PhD I worked on developing Bayesian methods for the analysis of circular (longitudinal) data in the social sciences, mostly using the embedding approach to circular data, specifically on models employing the projected normal (PN) distribution. A copy of the dissertation can be found [here].

The embedding approach models the circular location and spread are modeled simultaneously and is very flexible regarding the type of models that can be fit. Interpretation of the parameter estimates from these models is however challenging, so several subprojects focus on the development of interpretation tools.

PN regression models

Investigation of the performance of two MCMC algorithms for estimating PN regression models. In this project, we have also analysed data from an interpersonal circumplex using the PN regression model.

• Cremers, J., Mainhard, M.T. & Klugkist, I. (2018). Assessing a Bayesian Embedding Approach to Circular Regression Models. Methodology, 14, 69-81. [Full-text]

Several measures to make the interpretation of regression effects on the circle easier:

• Cremers, J. , Mulder, K.T. & Klugkist, I. (2018). Circular Interpretation of Regression Coefficients. British Journal of Mathematical and Statistical Psychology, 71(1), 75-95. [Full-text]

Introduction and comparison of tools that can be used to distinguish between accuracy and location effects in a PN regression model:

• Cremers, J. & Hernandez-Stumpfhauser, D. (unpublished) Indicators for effects on mean and variance in projected normal regression models for a circular outcome. [GitHub]

PN mixed-effects models

Application of a Bayesian PN mixed-effects model to several repeated measures datasets from an interpersonal circumplex. The focus lies on how a circular model enriches our understanding of this type of data and new tools are introduced to make the interpretation of effects from a PN mixed-effects model easier.

• Cremers, J., Pennings, H.J.M., Mainhard, M.T. & Klugkist, I. (2021) Circular Modelling of Circumplex Measurements for Interpersonal Behavior. Assessment, 28(2), 585-600. [Full-text]

Wrapped Normal and Cauchy regression

A Bayesian circular regression model based on the wrapping approach:

Cremers, J., Jansen, I., &, Klugkist, I. (unpublished) Bayesian Analysis of Circular Data Using the Wrapping Approach. [GitHub]

A tutorial on circular data in cognitive psychology

Tutorial that introduces the R-package bpnreg for Bayesian PN regression and mixed-effects models:

• Cremers, J. & Klugkist, I. (2018) One direction? A tutorial for circular data with examples in cognitive psychology. Frontiers in Psychology: Cognitive Science.[Full-text]

Cylindrical models for circumplex data.

Regression extension of four models for cylindrical data that are subsequently fit to circumplex data:

• Cremers, J., Pennings, H.J.M & Ley, C. (2020) Regression Models for Cylindrical Data in Psychology. Multivariate Behavioral Analysis, 55(6), 910-925. [Full-text]