Selection bias in linear mixed models

The paper investigates the consequences of sample selection in multilevel for mixed models, focusing on the random intercept two-level linear model under a selection mechanism acting at both hierarchical levels. The behavior of sample selection and the resulting biases on the regression coefficients and on the variance components are studied both theoretically and through a simulation study. Most theoretical results exploit the properties of Normal and Skew-Normal distributions. The analysis allows to outline a taxonomy of sample selection in the multilevel framework that can support the qualitative assessment of the problem in specific applications and the development of suitable techniques for diagnosis and correction.