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review-article

Fixed and random effects models

Published: 07 February 2012 Publication History

Abstract

Traditional linear regression at the level taught in most introductory statistics courses involves the use of ‘fixed effects’ as predictors of a particular outcome. This treatment of the independent variable is often sufficient. However, as research questions have become more sophisticated, coupled with the rapid advancement in computational abilities, the use of random effects in statistical modeling has become more commonplace. Treating predictors in a model as a random effect allows for more general conclusions—a great example being the treatment of the studies that comprise a meta‐analysis as random rather than fixed. In addition, utilization of random effects allows for more accurate representation of data that arise from complicated study designs, such as multilevel and longitudinal studies, which in turn allows for more accurate inference on the fixed effects that tend to be of primary interest. It is important to note the distinctions between fixed and random effects in the most general of settings, while also knowing the benefits and risks to their simultaneous use in specific yet common situations. WIREs Comput Stat 2012, 4:181–190. doi: 10.1002/wics.201
This article is categorized under:
1
Statistical Models > Linear Models
2
Statistical Models > Classification Models

References

[1]
McCullagh P, Nelder JA. Generalized Linear Models. 2nd ed. New York: Chapman and Hall; 1989.
[2]
Molenberghs G, Verbeke G. Models for Discrete Longitudinal Data. New York: Springer; 2005.
[3]
Neuhaus JM, Kalbfleisch JD, Hauck WW. A comparison of cluster‐specific and population‐averaged approaches for analyzing correlated binary data. Int Stat Rev 1991, 59:25–35.
[4]
McCulloch CE, Searle SR. Generalized, Linear and Mixed Models. New York: Wiley; 2001.
[5]
Laird NM, Ware JH. Random‐effects models for longitudinal data. Biometrics 1982, 38:963–974.
[6]
Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. New York: Springer‐Verlag; 2000.
[7]
Zucker DM, Lieberman O, Manor O. Improved small sample inference in the mixed linear model. J R Stat Soc B 2000, 62:827–838.
[8]
Harville DA. Maximum likelihood approaches to variance component estimation and to related problems. J Am Stat Assoc 1977, 72:320–338.
[9]
Harville DA. Bayesian inference for variance components using only error contrasts. Biometrika 1974, 61:383–385.
[10]
Dempster AP, Rubin RB, Tsutakawa RK. Estimation in covariance components models. J Am Stat Assoc 1981, 76:341–353.
[11]
Catellier DJ, Muller KE. Tests for Gaussian repeated measures with missing data in small samples. Stat Med 2000, 19:1101–1114.
[12]
Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 1997, 53:983–997.
[13]
Gomez EV, Schaalje GB, Fellingham GW. Performance of the Kenward‐Roger method when the covariance structure is selected using AIC and BIC. Commun Stat Simul Comput 2005, 34:377–392.
[14]
Skene SS, Kenward MG. The analysis of very small samples of repeated measurements I: an adjusted sandwich estimator. Stat Med 2010, 29:2825–2837.
[15]
Verbeke G, Molenberghs G. The use of score tests for inference on variance components. Biometrics 2003, 59:254–262.
[16]
Verbeke G, Lesaffre E. The effect of misspecifying the random effects distribution in linear mixed models for longitudinal data. Comput Stat Data Anal 1997, 23:541–556.
[17]
Gurka MJ, Edwards LJ, Muller KE, Kupper LL. Extending the Box‐Cox transformation to the linear mixed model. J R Stat Soc A 2006, 169:273–288.
[18]
Verbeke G, Lesaffre E. A linear mixed‐effects model with heterogeneity in the random‐effects population. J Am Stat Assoc 1996, 91:217–221.
[19]
Ho HJ, Lin TI. Robust linear mixed models using the skew t distribution with application to schizophrenia data. Biom J 2010, 52:449–469.
[20]
Cheng J, Edwards LJ, Maldonado‐Molina MM, Komro KA, Muller KE. Real longitudinal data analysis for real people: building a good enough mixed model. Stat Med 2010, 29:504–520.
[21]
Akaike H. A new look at the statistical model identification. IEEE Trans Autom Control 1974, AC‐19: 716–723.
[22]
Schwarz G. Estimating the dimension of a model. Ann Stat 1978, 6:461–464.
[23]
Gurka MJ. Selecting the best linear mixed model under REML. The American Statistician 2006, 60:19–26.
[24]
Edwards LJ, Muller KE, Wolfinger RD, Qaqish BF, Schabenberger O. An R2 statistic for fixed effects in the linear mixed model. Stat Med 2008, 27:6137–6157.
[25]
Jacqmin‐Gadda H, Sibillot S, Proust C, et al. Robustness of the linear mixed model to misspecified error distribution. Comput Stat Data Anal 2007, 51:5142–5154.
[26]
Gurka MJ, Edwards LJ, Muller KE. Avoiding bias in mixed model inference for fixed effects. Stat Med (Epub ahead of print; 2011).
[27]
Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika 1986, 73:13–22.
[28]
Gurka MJ, LoCasale‐Crouch J, Blackman JA. Long term cognition, achievement, socioemotional, and behavioral development of healthy late preterm infants. Arch Pediatr Adolesc Med 2010, 164:525–532.
[29]
Thompson SG, Sharp SJ. Explaining heterogeneity in meta‐analysis: a comparison of methods. Stat Med 1999, 18:2693–2708.
[30]
DerSimonian R, Laird N. Meta‐analysis in clinical trials. Control Clin Trials 1986, 7:177–188.
[31]
Brockwell SE, Gordon IR. A comparison of statistical methods for meta‐analysis. Stat Med 2001, 20:825–840.
[32]
DerSimonian R, Kacker R. Random‐effects model for meta‐analysis of clinical trials: an update. Contemp Clin Trials 2007, 28:105–114.
[33]
Hardy RJ, Thompson SG. A likelihood approach to meta‐analysis with random effects. Stat Med 1996, 15:619–629.
[34]
Morris CN. Parametric empirical Bayes inference—theory and applications. J Am Stat Assoc 1983, 78:47–55.
[35]
Follmann DA, Proschan MA. Valid inference in random effects meta‐analysis. Biometrics 1999, 55:732–737.
[36]
Sidik K, Jonkman JN. A comparison of heterogeneity variance estimators in combining results of studies. Stat Med 2007, 26:1964–1981.
[37]
Goldstein H. Multilevel Statistical Models. 3rd ed. London: Arnold; 2003.

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Information & Contributors

Information

Published In

cover image Wiley Interdisciplinary Reviews
Wiley Interdisciplinary Reviews   Volume 4, Issue 2
March/April 2012
114 pages
ISSN:1939-5108
EISSN:1939-0068
Issue’s Table of Contents

Publisher

John Wiley & Sons, Inc.

United States

Publication History

Published: 07 February 2012

Author Tags

  1. mixed models
  2. multilevel studies
  3. meta‐analysis
  4. longitudinal data

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