Multivariate Covariance Generalized Linear Models

TL;DR

This paper introduces multivariate covariance generalized linear models (McGLMs), a flexible framework for analyzing complex multivariate data with various correlation structures, accommodating non-normal responses and diverse data types.

Contribution

The paper presents a unified modeling framework for multivariate non-normal data, incorporating multiple correlation structures via a covariance link function and matrix linear predictor.

Findings

Successfully applied to count, mixed-type, and spatio-temporal data examples.

Provides an efficient Newton scoring algorithm based on quasi-likelihood.

Enables analysis of diverse multivariate data with complex dependencies.

Abstract

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated measures and longitudinal structures, and the third involves a spatio-temporal analysis of rainfall data. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modelled by means of a link function and a linear predictor. The models are fitted using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, spatial and spatio-temporal structures.