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When BLUE is not best: non-normal errors and the linear model

Published online by Cambridge University Press:  09 October 2018

Daniel K. Baissa  and
Carlisle Rainey
Daniel K. Baissa
Affiliation:
Department of Government, Harvard University, 1737 Cambridge St., Cambridge, MA 02138, USA
Carlisle Rainey*
Affiliation:
Department of Political Science, Florida State University, Room 531B, Bellamy Building, 113 Collegiate Loop, Tallahassee, FL 32306, USA
*
*Corresponding author. Email: [email protected]
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Abstract

Researchers in political science often estimate linear models of continuous outcomes using least squares. While it is well known that least-squares estimates are sensitive to single, unusual data points, this knowledge has not led to careful practices when using least-squares estimators. Using statistical theory and Monte Carlo simulations, we highlight the importance of using more robust estimators along with variable transformations. We also discuss several approaches to detect, summarize, and communicate the influence of particular data points.

Type
Original Articles
Information
Political Science Research and Methods , Volume 8 , Issue 1 , January 2020 , pp. 136 - 148
Copyright
Copyright © The European Political Science Association 2018 

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References

Anderson, R (2008) Modern Methods for Robust Regression. Thousand Oaks, CA: Sage.Google Scholar
Angrist, JD Pischke, J-S (2009) Mostly Harmless Econometrics: An Empiricist's Companion. Princeton, NJ: Princeton University Press.Google Scholar
Beaton, AE Tukey, JW (1974) The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics 16(2), 147–185.Google Scholar
Beck, N Katz, JN (1995) What to Do (and Not to Do) with Time-Series Cross-Section Data. American Political Science Reviewi 89(3), 634–647.Google Scholar
Berry, WD Feldman, S (1985) Multiple Regression in Practice. Quantitative Applications in the Social Sciences. Thousand Oaks, CA: Sage.Google Scholar
Box, GEP (1953) Non-Normality and Tests on Variances. Biometrika 40(3/4), 318–335.Google Scholar
Box, GEP Cox, DR (1964) An Analysis of Transformations. Journal of the Royal Statistical Society, Series B 26(2), 211–252.Google Scholar
Casella, G Berger, RL (2002) Statistical Inference 2nd ed. Pacific Grove, CA: Duxbury.Google Scholar
Clark, WR Golder, M (2006) Rehabilitating Duverger’s Theory: Testing the Mechanical and Strategic Modifying Effects of Electoral Laws. Comparative Political Studies 39(6), 679–708.Google Scholar
Dodge, Y (ed.) (1987) Statistical Data Analysis Based on the Ll-Norm and Related Methods. Amsterdam: North-Holland.Google Scholar
Efron, B (1981) Nonparametric Estimates of Standard Error: The Jackknife, the Bootstrap, and Other Methods. Biometrika 68(3), 589–599.Google Scholar
Freedman, DA (2006) On the So-Called “Huber Sandwich Estimator” and “Robust Standard Error”. The American Statistician 60(4), 299–302.Google Scholar
Gujarati, DN (2004) Basic Econometrics 4th ed. Boston, MA: McGraw Hill.Google Scholar
Harden, JJ Desmarais, BA (2011) Linear Models with Outliers: Choosing Between Conditional-Mean and Conditional-Median Methods. State Politics and Policy Quarterly 11(4), 371–389.Google Scholar
Huber, PJ (1964) Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics 35(1), 73–101.Google Scholar
Huber, PJ (1973) Robust Regression: Asymptotics, Conjectures, and Monte Carlo. The Annals of Statistics 1(5), 799–821.Google Scholar
Huber, PJ Ronchetti, EM (2009) Robust Statistics vol. 2nd. Hoboken, NJ: Wiley.Google Scholar
Jann, B (2010) ‘robreg: Stata Module Providing Robust Regression Estimators’. Available at http://ideas.repec.org/c/boc/bocode/s457114.html Google Scholar
King, G Roberts, ME (2014) How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It. Political Analysis 23(2), 159–179.Google Scholar
King, G, Tomz, M Wittenberg, J (2000) Making the Most of Statistical Analyses: Improving Interpretation and Presentation. American Journal of Political Science 44(2), 341–355.Google Scholar
Krueger, JS Lewis-Beck, MS (2008) Is OLS Dead? The Political Methodologist 15(2), 2–4.Google Scholar
Mira, A (1999) Distribution-Free Test for Symmetry Based on Bonferroni's Measure. Journal of Applied Statistics 26(8), 959–972.Google Scholar
Mooney, CZ Duval, RD (1993) Bootstrapping: A Nonparametric Approach to Statistical Inference. Quantitative Applications in the Social Sciences. Newbery Park, CA: Sage.Google Scholar
Rousseeuw, P, Croux, C, Todorov, V, Ruckstuhl, A, Salibian-Barrera, M, Verbeke, T, Koller, M Maechler, M (2016) ‘robustbase: Basic Robust Statistics’. R Package Version 0.92-6. Available at http://CRAN.R-project.org/package=robustbase Google Scholar
Rousseeuw, PJ (1984) Least Median of Squares Regression. The Journal of the American Statistical Association 79(388), 871–880.Google Scholar
Rousseeuw, PJ Yohai, V (1984) ‘Robust Regression by Means of S-Estimators’. In J Franke, W Hardle and D Martin (eds), Robust and Nonlinear Time Series Analysis, vol. 26, Lecture Notes in Statistics Springer US, 256–272. NY: Springer.Google Scholar
Train, KE (2009) Discrete Choice Methods with Simulation 2nd ed. New York: Cambridge University Press.Google Scholar
Venables, WN Ripley, BD (2002) Modern Applied Statistics with S. New York: Springer.Google Scholar
Western, B (1995) Concepts and Suggestions for Robust Regression Analysis. American Journal of Political Science 39(3), 786–817.Google Scholar
White, H (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48(4), 817–838.Google Scholar
Wooldridge, JM (2013) Introductory Econometrics: A Modern Approach 5th ed. Mason, OH: South-Western Cengage Learning.Google Scholar
Yohai, V (1987) High Breakdown-Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics 15(2), 642–656.Google Scholar
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