09: Behavior of Confidence Intervals for Ridge Shrinkage Parameters in Beta Regression Models

Thomas M. Menino Convention & Exhibition Center 

Shrinkage estimators are widely used to address multicollinearity in regression models, yet their inferential properties are not well understood beyond classical linear settings. This paper investigates the behavior of confidence intervals of ridge shrinkage parameters in beta regression models. We conducted a large-scale Monte Carlo simulation study under varying sample sizes, predictor dimensions, and levels of correlation among covariates. The parameters are evaluated using mean squared error, confidence interval width, and coverage probability. The results demonstrate that shrinkage estimators can substantially reduce estimation error relative to maximum likelihood estimation under moderate to severe multicollinearity. However, estimators with stronger shrinkage often exhibit noticeable undercoverage, whereas moderate shrinkage rules tend to achieve a more favorable balance between efficiency and coverage. These findings highlight important trade-offs between bias reduction and inferential accuracy. The results are particularly relevant for methodological development and applied analyses.

Multicollinearity

Beta Regression

Ridge Regression 

Biometrics Section