On Liu Estimators for the Logit Regression Model
AbstractIn innovation analysis the logit model used to be applied on available data when the dependent variables are dichotomous. Since most of the economic variables are correlated between each other practitioners often meet the problem of multicollinearity. This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Liu estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.
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Bibliographic InfoPaper provided by Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies in its series Working Paper Series in Economics and Institutions of Innovation with number 259.
Length: 14 pages
Date of creation: 18 Oct 2011
Date of revision:
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Postal: CESIS - Centre of Excellence for Science and Innovation Studies, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Phone: +46 8 790 95 63
Web page: http://www.infra.kth.se/cesis/
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Estimation; MAE; MSE; Multicollinearity; Logit; Liu; Innovation analysis;
Other versions of this item:
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
- C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-01 (All new papers)
- NEP-ECM-2011-11-01 (Econometrics)
- NEP-INO-2011-11-01 (Innovation)
- NEP-ORE-2011-11-01 (Operations Research)
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- Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
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