🤖 AI Summary
The application of the Nested Dirichlet distribution has been limited by the need to pre-specify a tree structure and the absence of effective diagnostic tools. This work proposes a data-driven greedy algorithm that, for the first time, enables automatic inference of the underlying tree structure. Furthermore, it introduces saddlepoint approximation–based pseudo-residuals and likelihood displacement measures, providing efficient model-fitting diagnostics even when marginal distributions are not analytically tractable. The method successfully identifies interpretable tree structures in both simulated data and real-world Morris water maze behavioral data, substantially improving model assessment accuracy. To facilitate reproducibility and broader adoption, the authors release an open-source R package implementing the proposed approach.
📝 Abstract
The Nested Dirichlet Distribution (NDD) provides a flexible alternative to the Dirichlet distribution for modeling compositional data, relaxing constraints on component variances and correlations through a hierarchical tree structure. While theoretically appealing, the NDD is underused in practice due to two main limitations: the need to predefine the tree structure and the lack of diagnostics for evaluating model fit. This paper addresses both issues. First, we introduce a data-driven, greedy tree-finding algorithm that identifies plausible NDD tree structures from observed data. Second, we propose novel diagnostic tools, including pseudo-residuals based on a saddlepoint approximation to the marginal distributions and a likelihood displacement measure to detect influential observations. These tools provide accurate and computationally tractable assessments of model fit, even when marginal distributions are analytically intractable. We demonstrate our approach through simulation studies and apply it to data from a Morris water maze experiment, where the goal is to detect differences in spatial learning strategies among cognitively impaired and unimpaired mice. Our methods yield interpretable structures and improved model evaluation in a realistic compositional setting. An accompanying R package is provided to support reproducibility and application to new datasets.