Confidence Interval Coverage in a Multicollinear Logistic Regression Model: A Simulation Study

Music City Center 

Multicollinearity refers to the condition where two or more independent variables show a strong correlation. Analyzing multicollinear data using generalized linear models (GLM) presents significant challenges. Highly correlated predictors cause the standard error estimates to inflate, resulting in wide confidence intervals, lower predictive power, and less reliable results for the maximum likelihood estimator (MLE) in GLM. Researchers have developed many methods to address the multicollinearity problem. Typically, the performance of various methods is compared based on their mean squared error (MSE). We aim to expand the research in this field for logistic regression (LR), focusing on the confidence intervals based on ridge, Liu, and Kibria–Lukman (KL) estimators. A simulation study examined the confidence intervals for estimates based on coverage probability and interval width in logistic regression under various conditions and for a range of shrinkage parameters. This paper is the first in the field to conduct a comparative study based on the coverage probability of confidence intervals in logistic regression.

Multicollinearity

logistic regression

shrinkage parameter

confidence interval

coverage probability 

Biometrics Section