Modelling Mixed Types of Outcomes in Additive Genetic Models

We present a general statistical modelling framework for handling multivariate mixed types of outcomes in the context of quantitative genetic analysis. The models are based on the multivariate covariance generalized linear models, where the matrix linear predictor is composed of an identity matrix combined with a relatedness matrix defined by a pedigree, representing the environmental and genetic components, respectively. We also propose a new index of heritability for non-Gaussian data. A case study on house sparrow (Passer domesticus) population with continuous, binomial and count outcomes is employed to motivate the new model. Simulation of multivariate marginal models is not trivial, thus we adapt the NORTA (Normal to anything) algorithm for simulation of multivariate covariance generalized linear models in the context of genetic data analysis. A simulation study is presented to assess the asymptotic properties of the estimating function estimators for the correlation between outcomes and the new heritability index parameters. The data set and R code are available in the supplementary material.