Sufficient dimension reduction for a novel class of zero-inflated graphical models

Eric Koplin, Liliana Forzani, Diego Tomassi and Ruth M. Pfeiffer

Computational Statistics & Data Analysis, 2024, vol. 196, issue C

Abstract: Graphical models allow modeling of complex dependencies among components of a random vector. In many applications of graphical models, however, for example microbiome data, the data have an excess number of zero values. New pairwise graphical models with distributions in an exponential family are presented, that accommodate excess numbers of zeros in the random vector components. First these multivariate distributions are characterized in terms of univariate conditional distributions. Then predictors that arise from such a pairwise graphical model with excess zeros are modeled as functions of an outcome, and the corresponding first order sufficient dimension reduction (SDR) is derived. That is, linear combinations of the predictors that contain all the information for the regression of the outcome as a function of the predictors are obtained. To incorporate variable selection, the SDR is estimated using a pseudo-likelihood with a hierarchical penalty that prioritizes sparse interactions only for variables associated with the outcome. These methods yield consistent estimators of the reduction and can be applied to continuous or categorical outcomes. The new methods are then illustrated by studying normal, Poisson and truncated Poisson graphical models with excess zeros in simulations and by analyzing microbiome data from the American Gut Project. The models provided robust variable selection and the predictive performance of the Poisson zero-inflated pairwise graphical model was equal or better than that of other available methods for the analysis of microbiome data.

Keywords: Count data; Hierarchical penalization; Hurdle model; Pairwise graphical models; Pseudo-likelihood; Variable selection (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947324000434
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:196:y:2024:i:c:s0167947324000434

DOI: 10.1016/j.csda.2024.107959

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().