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

Mengbing Li, Daniel Park, Maliha Aziz, Cindy M Liu, Lance Price, Zhenke Wu (2021+). Submitted
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This 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 binary weighted tree. Leaves in the given tree represent groups of observations with shorter distances between them indicating higher similarity. We propose a novel data integrative extension to classical latent class models (LCMs) with tree-structured shrinkage that enables 1) borrowing of information across leaf nodes, 2) data-driven groupings of observations 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 based on suboptimal use of the additional sample similarity information. We demonstrate the method by using mobile genetic elements to estimate the proportions of unobserved zoonotic E. coli isolates mapped over a phylogenetic tree which summarizes core-genome similarities. Model limitations and extensions are also discussed.

Keywords Gaussian Diffusion; Latent Class Models; Phylogenetic Tree; Zoonotic Infectious Diseases; Spike-and-Slab Prior; Variational Bayes.