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In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are random variables. In many applications including econometrics[1] and biostatistics[2][3][4][5][6] a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population.[7][6] Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity.
In panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).
^Greene, W.H., 2011. Econometric Analysis, 7th ed., Prentice Hall
^Diggle, Peter J.; Heagerty, Patrick; Liang, Kung-Yee; Zeger, Scott L. (2002). Analysis of Longitudinal Data (2nd ed.). Oxford University Press. pp. 169–171. ISBN 0-19-852484-6.
^Fitzmaurice, Garrett M.; Laird, Nan M.; Ware, James H. (2004). Applied Longitudinal Analysis. Hoboken: John Wiley & Sons. pp. 326–328. ISBN 0-471-21487-6.
^Laird, Nan M.; Ware, James H. (1982). "Random-Effects Models for Longitudinal Data". Biometrics. 38 (4): 963–974. doi:10.2307/2529876. JSTOR 2529876.
^Gardiner, Joseph C.; Luo, Zhehui; Roman, Lee Anne (2009). "Fixed effects, random effects and GEE: What are the differences?". Statistics in Medicine. 28 (2): 221–239. doi:10.1002/sim.3478. PMID 19012297. S2CID 16277040.
^ abGomes, Dylan G.E. (20 January 2022). "Should I use fixed effects or random effects when I have fewer than five levels of a grouping factor in a mixed-effects model?". PeerJ. 10: e12794. doi:10.7717/peerj.12794. PMC 8784019. PMID 35116198.
^Ramsey, F., Schafer, D., 2002. The Statistical Sleuth: A Course in Methods of Data Analysis, 2nd ed. Duxbury Press
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