As already mentioned, for some situations the formulation of and conduction of a precise mathematical treatment is often too difficult or too time-consuming. By using model-based simulation we may approximate real-world situations and results whenever the data is not sampled with a complex sampling design. Model-based simulation studies especially require much less time, effort, and/or money than a mathematical proof of properties of estimators or methods.
We will continue with the latent model from the previous example. Such datasets we may use for the comparison of methods. For example, one can mark values to be missing, impute them by suitable imputation methods and evaluate and compare the imputation methods. We can do this by example for a smaller dataset and compare mean imputation, nearest neighbor imputation, robust model-based imputation, and imputation by mice by using a simple precision-based error criterion based on...