Modeling of different covariance structures with the Bayesian method in repeated measurements in animal science

Repeated measurement analysis is a widely used design in animal science research. Standard regression and variance analysis methods do not meet the appropriate assumptions for repeated measurements. The models and methods to be applied for the analysis of these data have to define the relationship between the observations obtained from the same unit. For this reason and because of their correlation structure, there is a need to represent the repeated measures data with special statistical models and their complementary analysis methods. Mixed models provide more flexibility in modeling covariance structures for repeated measurement data and adequately explain the time-dependent correlations of units. Bayesian Monte Carlo methods offer a more effective alternative to other statistical methods such as Maximum Likelihood (ML). In order to compare the models, the Deviance Information Criteria (DIC) based on the relationship between the fit of the data to the model and the complexity of the model is proposed. This criteria, which uses the posterior distributions of the models obtained by the MCMC method, is useful in Bayesian model selection and used in many studies.It is important to make high-valid estimations on biological data such as body-weight and growth parameters by using appropriate statistical estimation methods. In this direction, the aim of the thesis study, which was determined as a result of literature reviews; To obtain solutions by modeling different covariance structures by using Bayesian analysis methods of repeated measurement analyses in the field of zootechnics and to show its applicability by using body-weight dataset. For this purpose, by modeling different covariance structures for informative prior and non-informative prior, and the most appropriate model was selected according to DIC value, and the results were interpreted.