Modeling and inference for Bayesian animal models in the presence of non-ignorable missing data.: The shared random effects method.
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Missing data in quantitative genetic studies of wild populations poses a non-trivial issue. To obtain unbiased inferences in the presence of non-ignorable missing data, it is necessary to model the joint distribution of missingness and the trait of interest, taking into account the phenotypes of those individuals that die prior to trait measurement. The present work propose an approach for the joint modeling of phenotypic data and missingness in the shared random effects framework, where a set of shared random effects, namely the breeding values, are assumed to induce their dependence. In general, models in quantitative genetics ignore the missing-data mechanism. A simulation study is conducted to evaluate the impact of various missing-data on parameter estimates obtained from such models. Efficient and accurate approximations to the posteriors can be obtained without simulation. Integrated nested Laplace approximation (INLA) is used as the method for Bayesian inference. The proposed methodology is used to analyze quantitative genetic properties of the trait body mass of a wild house sparrow population, and the trait spot diameter of a wild barn owl population. Inferences are also performed using the traditional methodology, an animal model, and results are compared. It is also described how the joint model can be extended to accommodate situations where the missingness relates to the trait of interest in different ways for males and females in a population.