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MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES.

Publication ,  Journal Article
Russo, M; Singer, BH; Dunson, DB
Published in: The annals of applied statistics
March 2022

Characterizing the shared memberships of individuals in a classification scheme poses severe interpretability issues, even when using a moderate number of classes (say 4). Mixed membership models quantify this phenomenon, but they typically focus on goodness-of-fit more than on interpretable inference. To achieve a good numerical fit, these models may in fact require many extreme profiles, making the results difficult to interpret. We introduce a new class of multivariate mixed membership models that, when variables can be partitioned into subject-matter based domains, can provide a good fit to the data using fewer profiles than standard formulations. The proposed model explicitly accounts for the blocks of variables corresponding to the distinct domains along with a cross-domain correlation structure, which provides new information about shared membership of individuals in a complex classification scheme. We specify a multivariate logistic normal distribution for the membership vectors, which allows easy introduction of auxiliary information leveraging a latent multivariate logistic regression. A Bayesian approach to inference, relying on Pólya gamma data augmentation, facilitates efficient posterior computation via Markov Chain Monte Carlo. We apply this methodology to a spatially explicit study of malaria risk over time on the Brazilian Amazon frontier.

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Published In

The annals of applied statistics

DOI

EISSN

1941-7330

ISSN

1932-6157

Publication Date

March 2022

Volume

16

Issue

1

Start / End Page

391 / 413

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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Chicago
ICMJE
MLA
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Russo, M., Singer, B. H., & Dunson, D. B. (2022). MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES. The Annals of Applied Statistics, 16(1), 391–413. https://doi.org/10.1214/21-aoas1496
Russo, Massimiliano, Burton H. Singer, and David B. Dunson. “MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES.The Annals of Applied Statistics 16, no. 1 (March 2022): 391–413. https://doi.org/10.1214/21-aoas1496.
Russo M, Singer BH, Dunson DB. MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES. The annals of applied statistics. 2022 Mar;16(1):391–413.
Russo, Massimiliano, et al. “MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES.The Annals of Applied Statistics, vol. 16, no. 1, Mar. 2022, pp. 391–413. Epmc, doi:10.1214/21-aoas1496.
Russo M, Singer BH, Dunson DB. MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES. The annals of applied statistics. 2022 Mar;16(1):391–413.

Published In

The annals of applied statistics

DOI

EISSN

1941-7330

ISSN

1932-6157

Publication Date

March 2022

Volume

16

Issue

1

Start / End Page

391 / 413

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 1403 Econometrics
  • 0104 Statistics