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

  • Daniel K. Baissa (a1) and Carlisle Rainey (a2)

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.

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Anderson, R (2008) Modern Methods for Robust Regression. Thousand Oaks, CA: Sage.
Angrist, JD Pischke, J-S (2009) Mostly Harmless Econometrics: An Empiricist's Companion. Princeton, NJ: Princeton University Press.
Beaton, AE Tukey, JW (1974) The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics 16(2), 147185.
Beck, N Katz, JN (1995) What to Do (and Not to Do) with Time-Series Cross-Section Data. American Political Science Reviewi 89(3), 634647.
Berry, WD Feldman, S (1985) Multiple Regression in Practice. Quantitative Applications in the Social Sciences. Thousand Oaks, CA: Sage.
Box, GEP (1953) Non-Normality and Tests on Variances. Biometrika 40(3/4), 318335.
Box, GEP Cox, DR (1964) An Analysis of Transformations. Journal of the Royal Statistical Society, Series B 26(2), 211252.
Casella, G Berger, RL (2002) Statistical Inference 2nd ed. Pacific Grove, CA: Duxbury.
Clark, WR Golder, M (2006) Rehabilitating Duverger’s Theory: Testing the Mechanical and Strategic Modifying Effects of Electoral Laws. Comparative Political Studies 39(6), 679708.
Dodge, Y (ed.) (1987) Statistical Data Analysis Based on the Ll-Norm and Related Methods. Amsterdam: North-Holland.
Efron, B (1981) Nonparametric Estimates of Standard Error: The Jackknife, the Bootstrap, and Other Methods. Biometrika 68(3), 589599.
Freedman, DA (2006) On the So-Called “Huber Sandwich Estimator” and “Robust Standard Error”. The American Statistician 60(4), 299302.
Gujarati, DN (2004) Basic Econometrics 4th ed. Boston, MA: McGraw Hill.
Harden, JJ Desmarais, BA (2011) Linear Models with Outliers: Choosing Between Conditional-Mean and Conditional-Median Methods. State Politics and Policy Quarterly 11(4), 371389.
Huber, PJ (1964) Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics 35(1), 73101.
Huber, PJ (1973) Robust Regression: Asymptotics, Conjectures, and Monte Carlo. The Annals of Statistics 1(5), 799821.
Huber, PJ Ronchetti, EM (2009) Robust Statistics vol. 2nd. Hoboken, NJ: Wiley.
Jann, B (2010) ‘robreg: Stata Module Providing Robust Regression Estimators’. Available at
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.
King, G, Tomz, M Wittenberg, J (2000) Making the Most of Statistical Analyses: Improving Interpretation and Presentation. American Journal of Political Science 44(2), 341355.
Krueger, JS Lewis-Beck, MS (2008) Is OLS Dead? The Political Methodologist 15(2), 24.
Mira, A (1999) Distribution-Free Test for Symmetry Based on Bonferroni's Measure. Journal of Applied Statistics 26(8), 959972.
Mooney, CZ Duval, RD (1993) Bootstrapping: A Nonparametric Approach to Statistical Inference. Quantitative Applications in the Social Sciences. Newbery Park, CA: Sage.
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
Rousseeuw, PJ (1984) Least Median of Squares Regression. The Journal of the American Statistical Association 79(388), 871880.
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.
Train, KE (2009) Discrete Choice Methods with Simulation 2nd ed. New York: Cambridge University Press.
Venables, WN Ripley, BD (2002) Modern Applied Statistics with S. New York: Springer.
Western, B (1995) Concepts and Suggestions for Robust Regression Analysis. American Journal of Political Science 39(3), 786817.
White, H (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48(4), 817838.
Wooldridge, JM (2013) Introductory Econometrics: A Modern Approach 5th ed. Mason, OH: South-Western Cengage Learning.
Yohai, V (1987) High Breakdown-Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics 15(2), 642656.
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Political Science Research and Methods
  • ISSN: 2049-8470
  • EISSN: 2049-8489
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