Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Abstract

Overweight and obesity in adults are known to be associated with risks of metabolic and cardiovascular diseases. Because obesity is an epidemic, increasingly affecting children, it is important to understand if this condition persists from early life to childhood and if different patterns of obesity growth can be detected. Our motivation starts from a study of obesity over time in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight patterns taken every 6 months from birth. We propose a novel model that facilitates clustering by combining a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show the superiority of the model to capture patterns, compared to other alternatives. We apply the model to the motivating dataset, and discuss the main features of the detected clusters. We also compare alternative models with ours in terms of predictive performances.

BayesMix: Bayesian Mixture Models in C++

“…Moreover, they are able to capture heterogeneity and to group data together into homogeneous clusters. The usefulness of mixture models, either finite or infinite, is evident from the huge literature developed around this topic, with applications in genomics (Elliott, De Iorio, Favaro, Adhikari, and Teh 2019), healthcare (Beraha, Guglielmi, Quintana, de Iorio, Eriksson, and Yap 2022), text mining (Blei, Ng, and Jordan 2003) and image analysis (Lü, Arbel, and Forbes 2020), to cite a few. See also Mitra and Müller (2015) for Bayesian nonparametric mixture models in biostatistical applications and the last five chapters in Fruhwirth-Schnatter et al (2019) for applications of mixture models to different contexts, including industry, finance, and astronomy.…”