ERIC Number: ED652789
Record Type: Non-Journal
Publication Date: 2023
Pages: 49
Abstractor: As Provided
ISBN: N/A
ISSN: N/A
EISSN: N/A
Available Date: N/A
Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data
Yuqi Gu; Elena A. Erosheva; Gongjun Xu; David B. Dunson
Grantee Submission, Journal of Machine Learning Research v24 p1-49 2023
Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of "Dimension-Grouped" MMMs (Gro-M[superscript 3]s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M[superscript 3]s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M[superscript 3]s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through applications to a functional disability survey dataset and a personality test dataset.
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED); National Institutes of Health (NIH) (DHHS); National Science Foundation (NSF), Division of Mathematical Sciences (DMS); National Science Foundation (NSF), Division of Social and Economic Sciences (SES)
Authoring Institution: N/A
IES Funded: Yes
Grant or Contract Numbers: R305D200015; R01ES027498; R01ES028804; 2210796; 2150601; 1846747
Author Affiliations: N/A