Estimation of variance components in linear mixed model with robust estimator

In this study, how to estimate the variance components of the linear mixed model with robust estimators is explained and an application is made on a real dataset. For this purpose, firstly, estimation methods of fixed, random effect and variance components in linear mixed model are mentioned. Then, outliers and diagnostics used to reveal outliers are introduced in the linear mixed model. In case of outliers, instead of removing outliers, robust estimation methods are used to reduce the impact of outliers on parameter estimates. In this thesis study, if there is an outlier in the linear mixed model or the distribution of the data is skewed, the robust estimators are emphasized. The algorithm steps required to obtain robust estimates of variance components in linear mixed model with design adaptive scale estimation (DAS) are explained. In the first part of the application, robust linear mixed model estimates of a small data set containing outliers in the literature are given. The main purpose of analyzing this data is to show that the robust prediction gives better results, especially in small samples, in case of outliers. In the second part of the application, the parameter estimates, variance components, genetic parameters and breeding values related to the eighth age values estimated with a robust linear mixed model in the Red Pine trees project in Antalya Region in the "National Tree Breeding Program" previously carried out by the General Directorate of Forestry.