Talk:Fixed effects model

Fixed effects model should be merged into this article, and the seemingly opposite descriptions on that page should either be harmonized or deleted if they simply represent an error. Torfason 14:39, 18 April 2007 (UTC)
 * YES. Jeremy Tobacman 10:48, 8 August 2007 (UTC)
 * I'm going ahead. Jeremy Tobacman 10:51, 8 August 2007 (UTC)

The article doesn't seem to be correct when it says "A random effects model makes the additional assumption that the individual effects are randomly distributed. It is thus not the opposite of a fixed effects model, but a special case." My understanding and what I have read elsewhere is that the random effects model is more general than the fixed effects model. Setting the variance of the effect to zero derandomizes the random effects and makes them fixed effects. I didn't change the article yet because I'm not familiar with the formalisms of this area yet. Thoughts? --Tekhnofiend (talk) 23:17, 3 March 2008 (UTC)

Add example of the shortcoming. E.g. cannot estimate Race, etc.

Add the matrix version of the estimator cancan101 (talk) 00:18, 20 February 2009 (UTC)

The Fixed and Random effect assumptions as stated were clearly wrong. The RE assumption is that the individual specific effect is uncorrelated with the regressors, not that it is just random. The difference is that if it is uncorrelated it can be added to the error of the model and estimated normally. The FE assumption is that the random effect is actually correlated with the regressors so that if you just added it to the error of the model there will be a problem with endogeneity. I also added the LD and FD estimators, a discussion about dummy variables, the hausman-taylor method, and the hausman test for testing RE vs. RE. The section about using dummy variables to estimate a fixed effect model should be expanded and there should be a section about correlated random effects. Mikethechampion (talk) 02:10, 5 May 2009 (UTC)

Needs Work/Contradicts?
I'm new to editing, so I want to suggest a two changes before making them. If there's no objection after a while, I'll edit the article.
 * First, I think it's important to emphasize the importance of categorical explanatory variables in this context. By traditional definitions, continuous explanatory variables are fixed effects, so it is only important to consider categorical variables and their interactions when deciding between a fixed and random/mixed effects model.  When we treat a categorical explanatory variable as a fixed effect, we assume that we have observed every category of interest.  When we treat it as a random effect, we assume that the categories follow a categorical distribution and we have only observed a small sample of all possible categories.
 * Second, the article uses the panel-data terminology subject-specific effects to refer to effects impacting groups of observations with the same value of a categorical explanatory variable. If multiple measurements are made on one subject it is correct to call this a subject-specific effect, but outside of panel/longitudinal data that's not generally true.  In the example of students' test scores given in Random effects model, each observation comes from a different individual student, and the effect of the school on the student's score is more accurately described as school-specific or group-specific, not subject-specific. --Maximillion Likelihood (talk) 00:02, 3 December 2014 (UTC)


 * There appears to me to be larger problem related to what you've said here, comments by Tekhnofiend and Executive Outcomes. It seems there two contradictory definitions for "fixed effects": The first definition contrasts fixed effects with random effects: random effects being a response that is a realization of a random variable; fixed effects being responses that don't arise from a random variable. The second definition is a set of parameters for a categorical variable (which is a subset of the first definition). The two definitions are not compatible, as pointed out by Tekhnofiend. By the first definition fixed effect and random effects models have no overlap, and are both subsets of mixed effects models. By the second definition, you could have a random, fixed effects model. This article is describing, for the most part, the second definition. The first definition is mentioned only briefly in the lead in. From my experience, the only field that uses the second definition is econometrics. The second definition is also at odds with multiple other articles on Wikipedia, ANOVA, mixed effects, random effects (except someone has unhelpfully added sentences explaining how "biostaticians" use the first definition to certain articles, including this one). That definition isn't limited to "biostatisticians" - I have seen multiple statistics (not econometrics) texts that use the first definition. Does anyone have a feeling for which definition is more common? I think the first definition is far older, dating to 1960 I believe by Tukey (who was a statistician, not a "biostatistician" or economist). I think, given the long history, apparent wide usage of the first definition, along with its consistent definition across multiple articles, this article should be written to describe the first definition, and the second definition should be explained as an alternative usage that is primarily used in econometrics and that is a special case of the first definition. 50.179.165.28 (talk) 14:17, 12 August 2015 (UTC)
 * I do not think that any experts use fixed effects to mean effects associated with categorical variables, although maybe a few misguided people do. Using it that way would not make sense.
 * Biostatisticians use it the same way as anyone else as far as I know. See this for example, https://biostatistics.letgen.org/mikes-biostatistics-book/anova-designs-multiple-factors/fixed-effects-random-effects/. The description is not exact, and probably one could take issue with it, but for one thing, it clearly aligns with the typical definition of fixed effects, and for another, it certainly does not mean a categorical variable. I've actually never seen anyone define a fixed effect as one associated with a categorical variable. Do you have a source for this? UsernamesEndedYearsAgo (talk) 20:29, 29 April 2024 (UTC)

This article seems to contradict several others related to it (random effects and ANOVA). If it doesn't, it's written poorly enough that it appears to. I deleted some of the random stuff about race (what?), but don't have the competence to attack the rest of the qualitative description. Help? Executive Outcomes (talk) 14:33, 21 July 2009 (UTC)

Also, the link "Distinguishing Between Random and Fixed: Variables, Effects, and Coefficients" now links to some university home page with no relation to this article Executive Outcomes (talk) 14:37, 21 July 2009 (UTC)

The notations $$ \perp $$ and  $$ \not \perp $$ need some explanation or at least a link to an explanation. Melcombe (talk) 14:31, 18 September 2009 (UTC)

Cleaned up the confusing notation. I think the apparent contradiction is because this article is written using econometrics jargon and the RE and ANOVA articles use statistics jargon. Someone needs to standardize these articles and connect all the fixed effects and random effects links. Perhaps this article should be titled, Fixed Effects Model so that it is symmetric with Random Effect Model. Mikethechampion (talk) 06:03, 5 November 2009 (UTC)


 * I have had the article renamed as suggested, and have rewritten the start of the lead correspondingly. Also I have removed the external link mentioned above as irrelevant. Melcombe (talk) 15:30, 9 November 2009 (UTC)

Short question about notation: why are the transformed variables in "Formal description" named e.g. $$\ddot{y}$$? In physics, this would mean the second time derivative of y, which as far as I understand is entirely different. 131.111.184.24 (talk) 10:56, 10 February 2015 (UTC)

Some example tables?
When learning about various regression techniques, I've had the most luck understanding things when an example table has been given. If there is a way to run a fixed effects regression, and present the results in a form similar to the output of a popular statistics tool, I think this would be incredibly helpful in understanding what fixed effects regressions are measuring. —Preceding unsigned comment added by 134.10.12.33 (talk) 21:09, 19 April 2010 (UTC)

I agree, an example would be very useful. See for example http://www.nyu.edu/its/pubs/connect/fall03/yaffee_primer.html. Even an example equation as in Random_effects_model would be good. dfrankow (talk) 19:20, 4 March 2011 (UTC)

Formal description --- difference between $$X_{it}$$ and $$x_{it}$$?
Is there a difference between $$X_{it}$$ and $$x_{it}$$ in the section Formal description? 129.247.247.240 (talk) 16:18, 14 January 2016 (UTC)


 * Then general convention in statistical notation is that a capitals such as $$X_{it}$$ refer to random variables, whereas lower case such as $$x_{it}$$ refers to observed values. Tayste (edits) 20:36, 14 January 2016 (UTC)

Dr. Farsi's comment on this article
Dr. Farsi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"The opening text is not exact: For the opening text I propose the following revision:

The original text: In statistics, a fixed effects model is a statistical model that represents the observed quantities in terms of explanatory variables that are treated as if the quantities were non-random. This is in contrast to random effects models and mixed models in which either all or some of the explanatory variables are treated as if they arise from random causes. Contrast this to the biostatistics definitions,[1][2][3][4] as biostatisticians use "fixed" and "random" effects to respectively refer to the population-average and subject-specific effects (and where the latter are generally assumed to be unknown, latent variables). Often the same structure of model, which is usually a linear regression model, can be treated as any of the three types depending on the analyst's viewpoint, although there may be a natural choice in any given situation.

I propose: 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 considered as random variables. In many applications including Econometrics (Greene, W.H., 2011. Econometric Analysis, 7th ed. Prentice Hall) and Biostatitistics[1][2][3][4], a fixed effect 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 (see for instance: Ramsey, F., Schafer, D., 2002. The Statistical Sleuth: A Course in Methods of Data Analysis, 2nd ed. Duxbury Press.). Generally, data can be grouped along 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.

Original text: 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. If we assume fixed effects, we impose time independent effects for each entity that are possibly correlated with the regressors.

I propose: 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).

In the following section (qualitative description): Original text: The random effects assumption (made in a random effects model) is that the individual specific effects are uncorrelated with the independent variables. The fixed effect assumption is that the individual specific effect is correlated with the independent variables.

I propose: Usually, the random effects assumption (made in a random effects model) is that the individual specific effects are uncorrelated with the independent variables. In the fixed effect model this assumption is relaxed."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Farsi has published scholarly research which seems to be relevant to this Wikipedia article:


 * Reference : Philippe K. Widmer & Peter Zweifel & Mehdi Farsi, 2011. "Accounting for heterogeneity in the measurement of hospital performance," ECON - Working Papers 052, Department of Economics - University of Zurich.

ExpertIdeasBot (talk) 18:51, 27 June 2016 (UTC)

Chamberlain's approach to unobserved effects models
As another method of estimating fixed effects models, it should be mentioned here. Furthermore, I think it should be merged here. Wikiacc (¶) 19:19, 27 October 2019 (UTC)
 * Merge request removed. The article is somewhat long, and it really doesn't need to be condensed. Wikiacc (¶) 02:05, 28 August 2020 (UTC)