A robust linear mixed-effects model for longitudinal data using an innovative multivariate skew-Huber distribution.

Conventional linear mixed-effects modeling is routinely challenging when the validity of necessary assumptions is suspicious. In particular, robustifying model fitting is appealing in the presence of potential outlying points. This paper introduces a robust regression methodology in a parametric setting by constructing a novel multivariate skew-Huber distribution for longitudinal data with heavy-tails and skewed structures. Unlike preceding studies, our model allows for jointly estimating the tuning parameter, which controls the impact of outliers, with all other parameters using an undemanding computational algorithm. Moreover, by promoting an unconstrained parameterization through the modified Cholesky decomposition, the estimate of variance–covariance components can be merely accessible. We also present a spline mixed model to account for the covariate effect. To highlight the usefulness of our methodology, we conducted a simulation study and analyzed a data set collected on type 2 diabetic patients with microalbuminuria over a 6-year prospective cohort study. Findings show that our proposed robust model leads to convincing conclusions in empirical studies. • Introduces the multivariate Huber distribution and studies its main properties. • Presents a robust regression mixed model to analyze correlated data when outliers exist. • Provides case weight for each subject through the tuning parameter estimate. • Offers an easy algorithm for jointly estimate the tuning parameter, variance–covariance components, and fixed effects. • Delivers direct parameterization by utilizing the modified Cholesky decomposition technique. We consider various correlation structures to the model specification. [ABSTRACT FROM AUTHOR]