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I understand that the assumption made in a fixed effects model is that there is a basic understanding of the included parameters, e.g. there is a proven theory or previous experiments have shown non-random effects of the parameters.

In a random effects model, however, a parameter is treated as a random variable. Effects are completely random samples form a larger population.

This leads to my question: Why, then, is the random effects model--at least according to Wikipedia (https://en.wikipedia.org/wiki/Random_effects_model) --considered a special case of the fixed effects model?

The random effects model is a special case of the fixed effects model.

To me, it more seems as if they are complete opposites.

amoeba
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mjbeyeler
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  • I think the sentence "The random effects model is a special case of the fixed effects model" is wrong. If at all, it should be the other way round: fixed effect can be seen as a random effect with zero variance. – amoeba Jun 19 '18 at 08:53
  • But is it always the case that fixed effects have zero variance? Also according to Wikipedia, a fixed effect can has non-random variability. This isn't the same as zero variance... – mjbeyeler Jun 19 '18 at 09:24
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    Two advices: (1) don't trust Wikipedia in this topic. (2) Look at the math, not at verbal descriptions. Then you will see what the difference really is. – amoeba Jun 19 '18 at 09:38
  • There are several good discussions of FE, RE, their relationship and the use(s) of these terms in different fields on this site. See, e.g., https://stats.stackexchange.com/questions/238214/how-exactly-does-a-random-effects-model-in-econometrics-relate-to-mixed-models, https://stats.stackexchange.com/questions/188349/use-of-fixed-effects-and-random-effects, https://stats.stackexchange.com/questions/4700/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode – Christoph Hanck Jun 19 '18 at 14:14
  • I think you mean: Random Effect Model is a special case of the Random Parameter Model. – Dr Neo Feb 19 '22 at 16:50

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