Performance of Some Logistic Ridge Regression Estimators

• Published in: Computational economics Vol. 40; no. 4; pp. 401 - 414
• Main Authors: Kibria, B. M. Golam, Månsson, Kristofer, Shukur, Ghazi
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-12-2012; Springer Nature B.V
• Subjects: Analysis; Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Economic performance; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Estimates; Estimation; Evaluation; Logit; Math Applications in Computer Science; Methods; MSE; Multicollinearity; Operations Research/Decision Theory; Regression analysis; Ridge regression; Simulation; Standard deviation; Statistical analysis; Statistics/Econometrics; Statistik; Studies; Variables; Ridge regression; Secondary 62F1Q; Simulation; Primary 62J07; Estimation; Multicollinearity; Logit; MSE
• ISSN: 0927-7099; 1572-9974; 1572-9974
• DOI: 10.1007/s10614-011-9275-x

In this paper we generalize different approaches of estimating the ridge parameter
k
proposed by Muniz et al. (Comput Stat,
2011
) to be applicable for logistic ridge regression (LRR). These new methods of estimating the ridge parameter in LRR are evaluated by means of Monte Carlo simulations along with the some other estimators of
k
that has already been evaluated by Månsson and Shukur (Commun Stat Theory Methods,
2010
) together with the traditional maximum likelihood (ML) approach. As a performance criterion we use the mean squared error (MSE). In the simulation study we also calculate the mean value and the standard deviation of
k
. The average value is interesting firstly in order to see what values of
k
that are reasonable and secondly if several estimators have equal variance then the estimator that induces the smallest bias should be chosen. The standard deviation is interesting as a performance criteria if several estimators of
k
have the same MSE, then the most stable estimator (with the lowest standard deviation) should be chosen. The result from the simulation study shows that LRR outperforms ML approach. Furthermore, some of new proposed ridge estimators outperformed those proposed by Månsson and Shukur (Commun Stat Theory Methods,
2010
).