Novel robust logistic regression estimators for effectively modeling of multivariate binary data under outliers and multicollinearity: application to heavy metal contamination data in Al-Kharj landfills

Logistic regression models are widely used for analyzing binary data, with the maximum likelihood estimator (MLE) being the standard method to estimate coefficients. However, the MLE becomes unstable and unreliable in the presence of multicollinearity or outliers. Outliers distort parameter estimates by unduly influencing the likelihood function, leading to bias and poor prediction. Multicollinearity inflates the variance of coefficients, reducing stability and interpretability. While biased estimators exist for multicollinearity and robust estimators for outliers, a unified framework that simultaneously handles both issues is still lacking. To address these issues, we have proposed a class of robust ridge-type estimators that combine robust logistic estimation with shrinkage methods. A comprehensive Monte Carlo simulation study evaluated the proposed estimators under varying levels of outliers and multicollinearity. Results show that our methods consistently outperform the traditional MLE and existing estimators in terms of accuracy and robustness. Finally, we demonstrated practical utility by analyzing heavy metal and metalloid contamination levels in landfill sites in Al-Kharj, Saudi Arabia, with empirical findings confirming that the proposed robust logistic estimators provide reliable and efficient inference when both multicollinearity and outliers are present.