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On Liu Estimators for the Logit Regression Model

Author

Listed:
  • Månsson, Kristofer

    (Jönköping University)

  • Kibria, B. M. Golam

    (Florida International University)

  • Shukur, Ghazi

    (Linnaeus University)

Abstract

In 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.

Suggested Citation

  • Månsson, Kristofer & Kibria, B. M. Golam & Shukur, Ghazi, 2011. "On Liu Estimators for the Logit Regression Model," Working Paper Series in Economics and Institutions of Innovation 259, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    • Handle: RePEc:hhs:cesisp:0259
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    Cited by:

    1. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.
    2. Iqra Babar & Hamdi Ayed & Sohail Chand & Muhammad Suhail & Yousaf Ali Khan & Riadh Marzouki, 2021. "Modified Liu estimators in the linear regression model: An application to Tobacco data," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-13, November.
    3. 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.
    4. Adewale F. Lukman & B. M. Golam Kibria & Cosmas K. Nziku & Muhammad Amin & Emmanuel T. Adewuyi & Rasha Farghali, 2023. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    5. M. Revan Özkale, 2016. "Iterative algorithms of biased estimation methods in binary logistic regression," Statistical Papers, Springer, vol. 57(4), pages 991-1016, December.
    6. N. H. Jadhav, 2020. "On linearized ridge logistic estimator in the presence of multicollinearity," Computational Statistics, Springer, vol. 35(2), pages 667-687, June.
    7. Ghazi Shukur & Kristofer Månsson & Pär Sjölander, 2015. "Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 539-550, December.
    8. Mohamed R. Abonazel & Rasha A. Farghali, 2019. "Liu-Type Multinomial Logistic Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 203-225, December.
    9. Özkale, M. Revan & Arıcan, Engin, 2015. "First-order r−d class estimator in binary logistic regression model," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 19-29.
    10. M. Arashi & T. Valizadeh, 2015. "Performance of Kibria’s methods in partial linear ridge regression model," Statistical Papers, Springer, vol. 56(1), pages 231-246, February.

    More about this item

    Keywords

    Estimation; MAE; MSE; Multicollinearity; Logit; Liu; Innovation analysis;
    All these keywords.

    JEL classification:

    • 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

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