Influence measures for L1 regression: an analysis with the R package diagL1

Identifying influential observations in $ L_1 $ L1 regression is crucial to ensuring the robustness of parameter estimates. However, influence diagnostics for $ L_1 $ L1 regression remain less explored compared to standard least squares regression, and existing measures have not been systematically reviewed or compared. To address this gap, we present a comprehensive review of five influence measures: likelihood displacement, conditional likelihood displacement, Cook's distance, and two additional measures. We introduce the R package diagL1, which provides tools for fitting $ L_1 $ L1 regression models and applying these influence measures. Through applications to lithogenic bile and pollution datasets, we illustrate the practical utility of these measures and demonstrate how diagL1 facilitates their implementation. The results highlight the relevance of these diagnostics in improving $ L_1 $ L1 regression analyses and guiding model assessment.