Bayesian zero-augmented Birnbaum–Saunders multilevel random effects model: an application to dietary consumption

Dietary research plays a crucial role in understanding the causes of various illnesses, and researchers often employ random effects models to effectively identify dietary patterns, considering multiple sources of variability. Modeling food intake data presents challenges due to the presence of zero values and potential asymmetry and heavy tails in the positive data. In this study, we addressed these challenges by proposing a novel approach using a zero-augmented Birnbaum–Saunders (ZABS) distribution parameterized by its mean and a scale parameter, incorporating random effects to accommodate variation due to repeated measures and experimental observations within a Bayesian framework. As part of the analysis we also fit a zero-augmented gamma model to the data, not as a primary goal for comparison, but to highlight that it may not be suitable in the presence of highly skewed data. Our results showed that the ZABS model presented better results in terms of both precision and goodness of fit, with this comparison studied specifically within the context of the real-world nutritional epidemiology dataset. Finally, the evaluation of different prior inputs for the covariance matrix of the random effects in prior sensitivity analysis provided valuable insights.