<p>The Birnbaum–Saunders distribution is commonly used to model lifetime data, particularly in reliability analysis. However, when multicollinearity exists among the predictor variables in the log Birnbaum–Saunders regression model, the maximum likelihood estimator (MLE) may yield biased and inefficient parameter estimates. To lessen the effect of multicollinearity, the study proposed the use of ridge regression instead of maximum likelihood estimation. We discussed the choice of the ridge parameters. We conducted a simulation study and a real-life application to evaluate the performance of the ridge regression estimator under different levels of multicollinearity. Furthermore, a SafeML-based predictive analysis confirms the superior generalization performance of the proposed ridge estimators compared to MLE under multicollinearity. We have compared the ridge regression results with those obtained from MLE and demonstrated the superiority of ridge regression in terms of lower MSE. The results imply that, in the presence of multicollinearity, ridge regression estimator provides more accurate and robust parameter estimations.</p>

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Addressing multicollinearity in log Birnbaum–Saunders regression model: a ridge regression estimation approach

  • Shahida Tabassum,
  • Saima Altaf

摘要

The Birnbaum–Saunders distribution is commonly used to model lifetime data, particularly in reliability analysis. However, when multicollinearity exists among the predictor variables in the log Birnbaum–Saunders regression model, the maximum likelihood estimator (MLE) may yield biased and inefficient parameter estimates. To lessen the effect of multicollinearity, the study proposed the use of ridge regression instead of maximum likelihood estimation. We discussed the choice of the ridge parameters. We conducted a simulation study and a real-life application to evaluate the performance of the ridge regression estimator under different levels of multicollinearity. Furthermore, a SafeML-based predictive analysis confirms the superior generalization performance of the proposed ridge estimators compared to MLE under multicollinearity. We have compared the ridge regression results with those obtained from MLE and demonstrated the superiority of ridge regression in terms of lower MSE. The results imply that, in the presence of multicollinearity, ridge regression estimator provides more accurate and robust parameter estimations.