Performance of Some Weighted Liu Estimators for Logit Regression Model: An Application to Swedish Accident Data

Abstract

In this article, we propose some new estimators for the shrinkage parameter d of the weighted Liu estimator along with the traditional maximum likelihood (ML) estimator for the logit regression model. A simulation study has been conducted to compare the performance of the proposed estimators. The mean squared error is considered as a performance criteria. The average value and standard deviation of the shrinkage parameter d are investigated. In an application, we analyze the effect of usage of cars, motorcycles, and trucks on the probability that pedestrians are getting killed in different counties in Sweden. In the example, the benefits of using the weighted Liu estimator are shown. Both results from the simulation study and the empirical application show that all proposed shrinkage estimators outperform the ML estimator. The proposed D9 estimator performed best and it is recommended for practitioners.

Keywords:

• Estimation
• Liu estimator
• Logit
• MSE
• Multicollinearity
• Simulation

Mathematics Subject Classification:

• Primary 62J07
• Secondary 62F10

Notes

When β₀ = 0, the dependent variable consists of, on average, around 50% ones; when β₀ = 1, the dependent variable consists of, on average, around 75% ones; and finally when β₀ = 2, the dependent variable consists of, on average, around 90% ones.

The data are available for the public on the webpage of the Department of Transport Analysis, www.trafa.se. The data are also available from the authors upon request.

The RSS is calculated as , where is the estimator of β obtained from either ML or weighted Liu and the marginal effects as , where is the jth element of .