A Solution to Errors-in-variables Bias in Multivariate Linear Regression using Compact Genetic Algorithms
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https://doi.org/10.53753/jame.2293Keywords:
Multivariate regression, Errors-in-variables, Compact genetic algorithmsAbstract
We address the classical errors-in-variables (EIV) problem in multivariate linear regression with N dependent variables where each left-hand-side variable is a function of a common predictor X subject to measurement error. Our contribution consists in employing the remaining N −1 regressions as extra information to obtain a filtered version of the mismeasured series X. We test the performance of our approach using simulations whereby we control for different cases like low vs. high R2 models, small vs. large sample or small vs. large measurement error variances. The results suggest that the multivariate-Compact Genetic Algorithm (mCGA) approach yields
estimates with lower mean-square-errors (MSEs). The MSEs are decreasing as the number of dependent variables increases. When there is no measurement error, our method gives results similar to those that would have been obtained by ordinary least-squares.
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Ashenfelter, O. and Krueger, A. (1994). Estimates of the economic returns to schooling from a new sample of twins. American Economic Review, 84(5):1157–73.
Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning.
Berkson, J. (1950). Are there two regressions? Journal of the Americal Statistical Association, 45(250):164–180.
Bound, J., Brown, C., and Mathiowetz, N. (2001). Measurement error in survey data. In Heckman, J. J. and Leamer, E. E., editors, Handbook of Econometrics, volume 5, pages 3705–3843. Elsevier. Section: 59.
Buonaccorsi, J. P. (2010). Measurement Error: Models, Methods, and Applications. Chapman & Hall.
Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. Chapman & Hall.
Chen, X., Hong, H., and Nekipelov, D. (2011). Nonlinear models of measurement errors. Journal of Economic Literature, 49(4):901–937.
Cheng, C.-L. and Van Ness, J. W. (1999). Statistical Regression with Measurement Error. Wiley.
Cragg, J. G. (1994). Making good inferences from bad data. Canadian Journal of Economics, 27(4):776–800.
Dagenais, M. G. and Dagenais, D. L. (1997). Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics, 76(1):193–221.
Davidson, R. and MacKinnon, J. G. (2004). Econometric Theory and Methods. Oxford University Press.
Diyarbakirlioglu, E., Desban, M., and Lajili-Jarjir, S. (2022). Asset pricing models with measurement error problems: A new framework with compact genetic algorithms. Finance, 43(2):1–78.
Durbin, J. (1954). Errors in variables. International Statistical Review, 22(1):23–32.
Feng, Z., Zhang, J., and Chen, Q. (2020). Statistical inference for linear regression models with additive distortion measurement errors. Statistical Papers, 61(6):2483–2509.
Frisch, R. (1934). Statistical confluence analysis by means of complete regression systems. Universitetets Okonomiske Instituut.
Fuller, W. A. (1987). Measurement Error Models. John Wiley & Sons, Inc.
Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc.
Griliches, Z. (1987). Economic data issues. In Griliches, Z. and Intriligator, M. D., editors, Handbook of Econometrics, volume 3, chapter 25, pages 1465–1514. Elsevier, 1 edition.
Harik, G. R., Lobo, F. G., and Goldberg, D. E. (1999). The compact genetic algorithm. IEEE Transactions on Evolutionary Computation, 3(4):287–297.
Harik, G. R., Lobo, F. G., and Sastry, K. (2006). Linkage Learning via Probabilistic Modeling in the Extended Compact Genetic Algorithm (ECGA), pages 39–61. Springer Berlin Heidelberg, Berlin, Heidelberg.
Harmon, C. and Walker, I. (1995). Estimates of the economic return to schooling for the united kingdom. American Economic Review, 85(5):1278–86.
Hausman, J. A. (2001). Mismeasured variables in econometric analysis: Problems from the right and problems from the left. Journal of Economic Perspectives, 15(4):57–67. Publisher: American Economic Association.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. University of Michigan Press.
Holland, J. H. (1987). Genetic algorithms and classifier systems: Foundations and future directions. In ICGA, pages 82–89.
Hyslop, D. R. and Imbens, G. W. (2001). Bias from classical and other forms of measurement error. Journal of Business & Economic Statistics, 19(4):475–481.
Klepper, S. and Leamer, E. E. (1984). Consistent sets of estimates for regressions with errors in all variables. Econometrica, 52(1):163–183.
Larranaga, P. (2002). A review on estimation of distribution algorithms. In Estimation of distribution algorithms, pages 57–100. Springer.
Pelikan, M., Goldberg, D. E., and Lobo, F. G. (2002). A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1):5–20.
Racicot, F.-E. (2015). Erreurs de mesure sur les variables ´economiques et financi`eres. La Revue des Sciences de Gestion, 3-4(267-268):79–103.
Satman, M. H. and Diyarbakirlioglu, E. (2015). Reducing errors-in-variables bias in linear regression using compact genetic algorithms. Journal of Statistical Computation and Simulation, 85(16):3216–3235.
Satman, M. H. and Diyarbakirlioglu, E. (2022). eive: An Algorithm for Reducing Errors-in-variables Bias in Linear Regression. R package version 3.1.0.
Shalabh, Garg, G., and Misra, N. (2010). Consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information. Statistical Papers, 51(3):717–748.
Wooldridge, J. M. (2010). Econometric Analysis of Cross-Section and Panel Data. MIT Press.
Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach. South-Western Cengage Learning.
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