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Fixed and random effects models: making an informed choice

Author

Listed:
  • Andrew Bell

    (University of Sheffield, ICOSS)

  • Malcolm Fairbrother

    (Umeå University)

  • Kelvyn Jones

    (University of Bristol)

Abstract

This paper assesses the options available to researchers analysing multilevel (including longitudinal) data, with the aim of supporting good methodological decision-making. Given the confusion in the literature about the key properties of fixed and random effects (FE and RE) models, we present these models’ capabilities and limitations. We also discuss the within-between RE model, sometimes misleadingly labelled a ‘hybrid’ model, showing that it is the most general of the three, with all the strengths of the other two. As such, and because it allows for important extensions—notably random slopes—we argue it should be used (as a starting point at least) in all multilevel analyses. We develop the argument through simulations, evaluating how these models cope with some likely mis-specifications. These simulations reveal that (1) failing to include random slopes can generate anti-conservative standard errors, and (2) assuming random intercepts are Normally distributed, when they are not, introduces only modest biases. These results strengthen the case for the use of, and need for, these models.

Suggested Citation

  • Andrew Bell & Malcolm Fairbrother & Kelvyn Jones, 2019. "Fixed and random effects models: making an informed choice," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 1051-1074, March.
    • Handle: RePEc:spr:qualqt:v:53:y:2019:i:2:d:10.1007_s11135-018-0802-x
    DOI: 10.1007/s11135-018-0802-x
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    as
    1. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    2. Cora J. M. Maas & Joop J. Hox, 2004. "Robustness issues in multilevel regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 127-137, May.
    3. Bell, Andrew & Jones, Kelvyn, 2015. "Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data," Political Science Research and Methods, Cambridge University Press, vol. 3(1), pages 133-153, January.
    4. Saïd Hanchane & Tarek Mostafa, 2012. "Solving endogeneity problems in multilevel estimation: an example using education production functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1101-1114, November.
    5. King, Gary & Roberts, Margaret E., 2015. "How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It," Political Analysis, Cambridge University Press, vol. 23(2), pages 159-179, April.
    6. Andrew Bell & Kelvyn Jones & Malcolm Fairbrother, 2018. "Understanding and misunderstanding group mean centering: a commentary on Kelley et al.’s dangerous practice," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(5), pages 2031-2036, September.
    7. Fotouhi, Ali Reza, 2003. "Comparisons of Estimation Procedures for Nonlinear Multilevel Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i09).
    8. Shor, Boris & Bafumi, Joseph & Keele, Luke & Park, David, 2007. "A Bayesian Multilevel Modeling Approach to Time-Series Cross-Sectional Data," Political Analysis, Cambridge University Press, vol. 15(2), pages 165-181, April.
    9. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    10. Nerlove,Marc, 2005. "Essays in Panel Data Econometrics," Cambridge Books, Cambridge University Press, number 9780521022460, November.
    11. Leckie, George & Charlton, Chris, 2013. "runmlwin: A Program to Run the MLwiN Multilevel Modeling Software from within Stata," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i11).
    12. Fiona Steele & Anna Vignoles & Andrew Jenkins, 2007. "The effect of school resources on pupil attainment: a multilevel simultaneous equation modelling approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(3), pages 801-824, July.
    13. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    14. Kelvyn Jones & Ron Johnston & David Manley & Dewi Owen & Chris Charlton, 2015. "Ethnic Residential Segregation: A Multilevel, Multigroup, Multiscale Approach Exemplified by London in 2011," Demography, Springer;Population Association of America (PAA), vol. 52(6), pages 1995-2019, December.
    15. Paul D. Allison, 1994. "Using Panel Data to Estimate the Effects of Events," Sociological Methods & Research, , vol. 23(2), pages 174-199, November.
    16. Jean-Bernard Chatelain & Kirsten Ralf, 2010. "Inference on Time-Invariant Variables using Panel Data: A Pre-Test Estimator with an Application to the Returns to Schooling," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00492039, HAL.
    17. Daniel Stegmueller, 2013. "How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches," American Journal of Political Science, John Wiley & Sons, vol. 57(3), pages 748-761, July.
    18. Andrew Bell & Ron Johnston & Kelvyn Jones, 2015. "Stylised fact or situated messiness? The diverse effects of increasing debt on national economic growth," Journal of Economic Geography, Oxford University Press, vol. 15(2), pages 449-472.
    19. Kerry Ard & Malcolm Fairbrother, 2017. "Pollution Prophylaxis? Social Capital and Environmental Inequality," Social Science Quarterly, Southwestern Social Science Association, vol. 98(2), pages 584-607, June.
    20. Milner, Helen V. & Kubota, Keiko, 2005. "Why the Move to Free Trade? Democracy and Trade Policy in the Developing Countries," International Organization, Cambridge University Press, vol. 59(1), pages 107-143, January.
    21. Thomas Herndon & Michael Ash & Robert Pollin, 2014. "Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 38(2), pages 257-279.
    22. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    23. Beck, Nathaniel & Katz, Jonathan N., 1995. "What To Do (and Not to Do) with Time-Series Cross-Section Data," American Political Science Review, Cambridge University Press, vol. 89(3), pages 634-647, September.
    24. Schurer, S. & Yong, J., 2012. "Personality, well-being and the marginal utility of income: What can we learn from random coefficient models?," Health, Econometrics and Data Group (HEDG) Working Papers 12/01, HEDG, c/o Department of Economics, University of York.
    25. Duncan, Craig & Jones, Kelvyn & Moon, Graham, 1996. "Health-related behaviour in context: A multilevel modelling approach," Social Science & Medicine, Elsevier, vol. 42(6), pages 817-830, March.
    26. Sylvie Goetgeluk & Stijn Vansteelandt, 2008. "Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data," Biometrics, The International Biometric Society, vol. 64(3), pages 772-780, September.
    27. Fairbrother, Malcolm, 2014. "Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey Datasets," Political Science Research and Methods, Cambridge University Press, vol. 2(1), pages 119-140, April.
    28. Zhang, Zhengzheng & Parker, Richard M. A. & Charlton, Christopher M. J. & Leckie, George & Browne, William J., 2016. "R2MLwiN: A Package to Run MLwiN from within R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i10).
    29. Croissant, Yves & Millo, Giovanni, 2008. "Panel Data Econometrics in R: The plm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i02).
    30. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    31. Katja Möhring & Alexander Schmidt, 2012. "Multilevel tools," German Stata Users' Group Meetings 2012 06, Stata Users Group.
    32. John M. Neuhaus & Charles E. McCulloch, 2006. "Separating between‐ and within‐cluster covariate effects by using conditional and partitioning methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 859-872, November.
    33. Croissant, Yves & Millo, Giovanni, 2008. "Panel Data Econometrics in R: The plm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i02).
    34. Bruno ARPINO & Roberta VARRIALE, 2010. "Assessing The Quality Of Institutions’ Rankings Obtained Through Multilevel Linear Regression Models," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 5(1(11)_Spr), pages 7-22.
    35. Brumback, Babette A. & Dailey, Amy B. & Brumback, Lyndia C. & Livingston, Melvin D. & He, Zhulin, 2010. "Adjusting for confounding by cluster using generalized linear mixed models," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1650-1654, November.
    36. Yongyun Shin & Stephen W. Raudenbush, 2010. "A Latent Cluster-Mean Approach to the Contextual Effects Model With Missing Data," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 26-53, February.
    37. N Bullen & K Jones & C Duncan, 1997. "Modelling Complexity: Analysing Between-Individual and Between-Place Variation—A Multilevel Tutorial," Environment and Planning A, , vol. 29(4), pages 585-609, April.
    38. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    39. Stephen W. Raudenbush & JDouglas Willms, 1995. "The Estimation of School Effects," Journal of Educational and Behavioral Statistics, , vol. 20(4), pages 307-335, December.
    40. Beck, Nathaniel & Katz, Jonathan N., 2007. "Random Coefficient Models for Time-Series—Cross-Section Data: Monte Carlo Experiments," Political Analysis, Cambridge University Press, vol. 15(2), pages 182-195, April.
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