Comparison of Test Statistics in the Ridge Probit Regression Model: Simulation and Application

Oregon Convention Center 

Ridge regression is a method that has been proposed to solve the multicollinearity problem in both linear and non-linear regression models. This paper studies different Ridge regression z-type tests of the individual coefficients for the Probit regression model. A simulation study was conducted to evaluate and compare the performance of the test statistics with respect to their empirical size and power under different simulation conditions. Our simulations identified which of the proposed tests maintain type I error rates close to the 5% nominal level while simultaneously showing gains in statistical power over the standard Wald z-test commonly used in Probit regression models. Our paper is the first of its kind to compare z-type tests for these different shrinkage approaches to estimation in Probit Ridge regression. The results will be valuable for applied statisticians and researchers in the area of regression models.

Poisson regression

Ridge regression

Liu regression

Kibria-Lukman regression

Empirical power

Type I error rate 

Biometrics Section