Integrating Sample Similarities into Latent Class Analysis: A Tree-Structured Shrinkage Approach

Abstract

SummaryThis paper is concerned with using multivariate binary observations to estimate the proportions of unobserved classes with scientific meanings. We focus on the setting where additional information about sample similarities is available and represented by a rooted weighted tree. Every leaf in the given tree contains multiple independent samples. Shorter distances over the tree between the leaves indicate higher similarity. We propose a novel data integrative extension to classical latent class models (LCMs) with tree-structured shrinkage. The proposed approach enables 1) borrowing of information across leaves, 2) estimating data-driven leaf groups with distinct vectors of class proportions, and 3) individual-level probabilistic class assignment given the observed multivariate binary measurements. We derive and implement a scalable posterior inference algorithm in a variational Bayes framework. Extensive simulations show more accurate estimation of class proportions than alternatives that suboptimally use the additional sample similarity information. A zoonotic infectious disease application is used to illustrate the proposed approach. The paper concludes by a brief discussion on model limitations and extensions.

Tree-informed Bayesian multi-source domain adaptation: cross-population probabilistic cause-of-death assignment using verbal autopsy

“…, G} for each c. The prior is based on a logistic stick-breaking Gaussian process, diffused along a pre-specified rooted weighted domain tree with G + 1 leaves that encodes external between-domain similarity information. Also see Appendix E in the Supplementary Materials for a review of the general statistical strategy of specifying tree-structured shrinkage priors (Thomas et al, 2020;Li et al, 2021a) .…”

“…The prior encourages collapsing certain parts of the tree so that observations within a collapsed leaf group share the same parameter value. Li et al (2021a) has extended Thomas et al (2020) to deal with rooted weighted trees. We specify a spike-and-slab Gaussian diffusion process prior along a rooted weighted tree for ϑ v .…”