Diagnostic analysis in scale mixture of skew-normal linear mixed models

Detecting influential observations and verifying their impact on model fitting and parameter estimation are essential steps in statistical modeling. Different approaches can be utilized to that end, including the case-deletion method, which evaluates the individual impact on the estimation process, and the local influence approach, which investigates the model sensitivity under some perturbation. This paper introduces case-deletion measures and influence diagnosis for a flexible class of longitudinal models, the scale mixture of skew-normal linear mixed models. This approach includes skewed and heavier-than-normal-tailed distributions while accounting for useful within-subject dependence structures. The method's capability of detecting atypical observations under repeated measurements and the impact of outliers on parameter estimation from models accounting for different distributions are evaluated in simulation studies and a real data illustration.