Two Levels Analysis with Skew Normal Random Effects and Modeling of Longitudinal Data

In two level modeling، random effect and error''s normality assumption is one of the basic assumptions. Violating this assumption leads to incorrect inference about coefficients of the model. In this paper، to resolve this problem، we use skew normal distribution instead of normal distribution for random and error components. Also، we show that ignoring positive (negative) skewness in the model causes overestimating (underestimating) in intercept estimation and underestimating (overestimating) in slope estimation by a simulation study. Finally، we use this model to study relationship between shift work and blood cholesterol.