Multivariate Generalized Linear Models for Twin and Family Data

Multivariate twin and family studies are one of the most important tools to assess diseases inheritance as well as to study their genetic and environment interrelationship. The multivariate analysis of twin and family data is in general based on structural equation modelling or linear mixed models that essentially decomposes sources of covariation as originally suggested by  Fisher. In this paper, we propose a flexible and unified statistical modelling framework for analysing multivariate Gaussian and non-Gaussian twin and family data. The non-normality is taken into account by actually modelling the mean and variance relationship, while the covariance structure is modelled by means of a linear covariance model including the option to model the dispersion components as functions of known covariates in a regression model fashion. The marginal specification of our models allows us to extend classic models and biometric indices such as the bivariate heritability, genetic, environmental and phenotypic correlations to non-Gaussian data. We illustrate the proposed models through simulation studies and six data analyses and provide computational implementation in R through the package mglm4twin.