Sandwich Variance Estimation in Scale Mixture of Skew-Normal Linear Mixed Models

Linear mixed models are often used to analyze studies with repeated measurements over time, where the data present a correlation between observations of the same individual. However, one of the main challenges in using these models is correctly defining the covariance structure associated with error and random effects. To overcome this challenge, we obtain the sandwich variance estimator as a robust alternative to estimate the standard error in the scale mixture of skew-normal linear mixed models (SMSN-LMMs). By definition, SMSN-LMMs can accommodate skewness and heavy tails, and by considering our proposed variance estimator, we increase the model's flexibility by allowing for misspecification of the covariance components. We present the definition of the estimator, its derivation for this model, and its practical implementation. In addition, through simulation studies, we evaluate its performance in different scenarios, demonstrating its ability to provide reliable inferences even when the model or the covariance structure is misspecified.