Development of Cook’s Distance and DFFITs Measures Based on Robust-M Kibria–Lukman Estimator for Detecting Influential Observations
Abstract
Identifying influential observations is crucial in regression analysis because such points can distort parameter estimates, prediction accuracy, and overall statistical inference. Traditional diagnostics such as Cook’s Distance and DFFITs, developed under the Ordinary Least Squares (OLS) framework, perform poorly when multicollinearity and outliers coexist. This study develops two new influential diagnostic measures—Cook’s Distance in Robust-M Kibria-Lukman (Cooks_KL_M) and DFFITs in Robust-M Kibria-Lukman (DFFITs_KL_M)—derived within the Robust-M KL estimator to simultaneously accommodate outliers and multicollinearity. Approximate deletion formulas for both measures are also established using the Sherman–Morrison–Woodbury identity. The proposed diagnostics are evaluated using two real datasets characterized by severe multicollinearity and outliers. Results reveal that Cooks_KL_M performs comparably with existing diagnostics, while DFFITs_KL_M exhibits enhanced sensitivity, detecting additional influential points overlooked in previous studies. These findings demonstrate that integrating robustness with shrinkage parameters enhances diagnostic performance, offering practitioners a more reliable tool for analyzing complex datasets.