Residual and influence analysis in linear mixed and hierarchical models

Statistical models are used for the identification of the data, the determination of the mathematical form that best represents the data structure and the definition approximately the relationship between the variables. Although the most widely-used statistical model is the ordinary linear regression model, it is sometimes possible to encounter with the data structures that accord with the models that include both fixed and random effects. In this case, linear mixed models and hierarchical linear models, which is one of the linear mixed model types that has nested data structure, are arised. In this study firstly, residual and influence analysis in linear regression models is emphasized in order to understand the residual and influence analysis in linear mixed and hierarchical models. Later, linear mixed model types, parameter estimates and update formulas of linear mixed models, examination of the residuals for searching estimated model validity, generalized leverage matrix that is considered to be useful for the identification of influential units and observations in linear mixed models, measures developed for the identification of influential observations in linear mixed models and last, residual analysis in hierarchical linear models are emphasized, respectively. The study is supported with examples done using R and Matlab programs.