Influence diagnostic in linear mixed measurement error models with stochastic linear restrictions

This article focuses on influence diagnostics in linear mixed models where the fixed effects are evaluated with error and subject to stochastic linear restrictions on the fixed and random effects, utilizing Nakamura’s (Citation1990) corrected likelihood. We explore the presence of outliers through mean shift analysis and investigate influential observations using case deletion models. Then, Cook’s distance, Likelihood distance, and Welsch’s distance are proposed as tools for influence diagnostics based on case deletion measures. We conducted a simulation study to evaluate the performance of the proposed score test statistics. We also used a parametric bootstrap to get the empirical distributions of the test statistics. Finally, we showed a real data example to examine how the influence measures perform.