A general algorithm for covariance modeling of discrete data

Gordana C. Popovic*, Francis K.C. Hui, David I. Warton

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    We propose an algorithm that generalizes to discrete data any given covariance modeling algorithm originally intended for Gaussian responses, via a Gaussian copula approach. Covariance modeling is a powerful tool for extracting meaning from multivariate data, and fast algorithms for Gaussian data, such as factor analysis and Gaussian graphical models, are widely available. Our algorithm makes these tools generally available to analysts of discrete data and can combine any likelihood-based covariance modeling method for Gaussian data with any set of discrete marginal distributions. Previously, tools for discrete data were generally specific to one family of distributions or covariance modeling paradigm, or otherwise did not exist. Our algorithm is more flexible than alternate methods, takes advantage of existing fast algorithms for Gaussian data, and simulations suggest that it outperforms competing graphical modeling and factor analysis procedures for count and binomial data. We additionally show that in a Gaussian copula graphical model with discrete margins, conditional independence relationships in the latent Gaussian variables are inherited by the discrete observations. Our method is illustrated with a graphical model and factor analysis on an overdispersed ecological count dataset of species abundances.

    Original languageEnglish
    Pages (from-to)86-100
    Number of pages15
    JournalJournal of Multivariate Analysis
    Volume165
    DOIs
    Publication statusPublished - May 2018

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