A Suggested Biased Estimator for Correcting Multicollinearity in Multinomial Logistic Regression | ||||
| The Egyptian Statistical Journal | ||||
| Article 5, Volume 58, Issue 2, December 2014, Page 183-197 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2014.314448 | ||||
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| Abstract | ||||
| Multinomial logistic model suffers from multicollinearity that causes wider confidence intervals and incorrect decisions for testing hypotheses for the regression parameters. Biased estimators were used for correcting multicollinearity in linear regression, binomial logistic and recently multinomial logistic regression [2,8,11,12]. This paper introduces a new biased estimator for the multinomial logistic regression model. This estimator is an extension of Liu biased estimator [18], which originally was developed for correcting multicollinearity in linear regression model and then extended by Mansson et al., [19] for the binomial logistic regression model. The suggested biased estimator combines the advantages of Stien estimators and ridge regression estimators, which are: 1) reducing the mean square errors (MSES) for the estimates of the parameters, and 2) improving the conditioning of the estimated weighted information matrix in multinomial logistic regression. So it is expected that the performance of the suggested biased estimator would be better than other biased estimators. A procedure of the successive steps for determining the suggested biased estimator is introduced. Using a data set comparison between the results of applying the suggested biased estimator with the results of applying the existing estimators (multinomial logistic Stien estimators and multinomial logistic ridge regression estimators) show that the suggested biased estimator is superior in terms of a reduction in the variances of the multinomial logistic regression estimates and also a reduction in the Mean Squared Errors of Responses (MSER). | ||||
| Keywords | ||||
| Biased Estimators; Multicollinearity - Multinomial Logistic Regression - Multinomial Stien Estimates - Multinomial Ridge Regression | ||||
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