In this paper we propose a strategy for robust estimation of a simple linear mixed model. The proposition is based on a regression depth function introduced by Rousseeuw and Hubert. We study the performance of the proposition on various two-dimensional data sets containing outliers. The Monte Carlo study shows the proposed estimator to have very good properties. Our study also shows the strategy we have put forth to have very good properties in comparison with a generalised least squares estimator on a real data set example concerning the relation between two economic variables considered in a regional classification.
The article presents two examples of causal inferences in which theoretical problems exclude a possibility to infer causal relations from effects of experimental manipulation. The first example is a causal inference through mediation analysis. Particular emphasis has been placed on interpretation of direct, total and indi¬rect effects in Structural Equation Modelling. The second example concerns the causal impact of a dependent variable on its own explanatory model. In this example estimation of the causal model parameters can be done through the Linear Mixed Model.
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