Ridge Estimators for Probit Regression: With an Application to Labour Market Data

Abstract

In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.

Two‐parameter estimation forTobitmodel: An application to national health and nutrition examination survey dataset

“…The primary of these articles can be given as follows: Hoerl, 6 Hoerl and Kennard, 7 Kibria, 8 Mansson et al, 9 Khalaf et al, 10 and Kibria and Lukman. 11 For logistic regression model, some of the papers related to ridge regression are Schaefer et al, 12 Lee and Silvapulle, 13 Le Cessie and Houwelingen, 14 Mansson and Shukur, 15 Kibria et al, 16 Asar et al 17 and Özkale et al 18 Kibria and Saleh, 19 Locking et al, 20,21 and Asar and K𝚤l𝚤nç 22 are the articles in which ridge regression is examined for the probit regression model. Khalaf et al 23 proposed ridge regression for the Tobit regression model while Ayd𝚤n et al 24 offered optimum shrinkage parameter selection for ridge type estimator in this model.…”