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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.

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  • $\begingroup$ 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. $\endgroup$
    – amoeba
    Jun 19, 2018 at 8:53
  • $\begingroup$ 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... $\endgroup$
    – mjbeyeler
    Jun 19, 2018 at 9:24
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    $\begingroup$ 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. $\endgroup$
    – amoeba
    Jun 19, 2018 at 9:38
  • $\begingroup$ 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., stats.stackexchange.com/questions/238214/…, stats.stackexchange.com/questions/188349/…, stats.stackexchange.com/questions/4700/… $\endgroup$
    – Christoph Hanck
    Jun 19, 2018 at 14:14
  • $\begingroup$ I think you mean: Random Effect Model is a special case of the Random Parameter Model. $\endgroup$
    – Dr Neo
    Feb 19, 2022 at 16:50

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