A Bayesian longitudinal circular model and model selection

Çamlı, Onur
This research was motivated by a recent medical study that aims to estimate the general fetal head progression trajectory during the first stage of normal labour adjusted for maternal characteristics and environmental factors. A rather primitive manual method for determining the progression has recently been replaced by an ultrasound technology that can precisely measure the fetal's head angle. The particular challenge with such data is the model selection procedures that could objectively assess the models when outcome data are longitudinal and circular. A Bayesian random intercept model on the circle was considered and the current model selection methods used in Bayesian analysis of circular data were reviewed and commented. Then criteria based on minimizing a predictive loss was focused and some new methods and new extensions to a current method were proposed. Extensive Monte Carlo simulation studies controlled for the sample size and intraclass correlation were used to study the performances of the model and these model selection criteria under various realistic longitudinal settings. Relative bias and mean square error were used to evaluate the performance of the estimators under correctly specified models and robustness to model misspecification. Several quantities were used to evaluate the performances of the model selection criteria such as frequency of selecting the true model and a ratio that measures the strength of the particular selection. Simulations reveal a noticeable or equivalent gain in performance achieved by the proposed methods. A conventional longitudinal data set (sandhopper data) was used to further compare the Bayesian model selection methods for circular data. This research hopes to address and contribute to the model selection in circular data, a rather fertile area for methodological and theoretical development, while the demand increases with the advancing technology as seen in our motivating data set.