Challenging Gaussian Assumptions in RPE Data: A Bayesian Comparison of Proportional Odds and Gaussian Models
Madeline Miller
Supervisor: Prof Chris Drovandi
Rating of perceived exertion (RPE) is a subjective scale widely used in sports science to measure exercise intensity. Many studies within this field assume RPE follows a Gaussian distribution, despite violating the discrete and bounded nature of RPE data. This can lead to inaccurate inferences derived from the model, compromising the validity of findings in these studies. In this study, we propose the proportional odds model as a more suitable alternative and compare it using statistical model selection tools to the commonly used Gaussian model for RPE data. To test this, we fitted proportional odds and Gaussian models to several RPE datasets in a Bayesian framework. Model performance was assessed through predictive posterior checks of cumulative distribution functions (CDFs), and the Widely Applicable Information Criterion (WAIC).
Our analysis showed that the proportional odds model consistently outperformed the Gaussian model, with lower WAIC values and a closer fit to the empirical CDF of the data. This indicates that not only does the proportional odds model better fit the observed data, but it also has higher predictive accuracy for unseen data. Furthermore, the two models yielded differing conclusions regarding variables of interest, further highlighting the importance of model selection in ensuring the validity of results.
These findings emphasise the importance of appropriate model selection in RPE studies, as the common assumption of a Gaussian distribution can lead to inaccurate conclusions.
