What is a fixed effect in a mixed model compared to a fixed effect model for panel data? [duplicate]

I am confused about the expression "fixed effect" in the context of mixed models. I am more familiar with the terms like "fixed effects" and "random effects" in context of econometrics and the analysis of panel data.

The understanding of "random effects" seems similar in both disciplines and the "random effects model" in econometrics is equivalent to a "mixed model with random intercept". See for example: How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?

But what is about the "fixed effect". In econometrics, with the help of fixed effects e.g. all time invariant effects will be absorbed. Or in other words, a dummy variable for each individual is introduced.

But, what is "fixed effect" in context of mixed models? In simple words? Hereby, I mean more the intuition and not the mathematically way.

It is not the same as a fixed effect in econometrics. That is what I understand, but I have no clue what it is instead.

EDIT:

Meanwhile I found this explanation in context of mixed models:

"The fixed effects are analogous to standard regression coefficients and are estimated directly."

This means to me, that a fixed effect in mixed models is not the same as fixed effects in econometrics. Or in other words: Fixed effects are the variables that are not declared as random effects (--> standard regression coefficients as in linear regression).

Source (slide 2): http://fmwww.bc.edu/EC-C/S2013/823/EC823.S2013.nn07.slides.pdf

marked as duplicate by amoeba, kjetil b halvorsen, mdewey, Peter Flom♦Dec 7 '17 at 12:51

• I think this is fully answered in the thread you linked to (even in the question itself). – amoeba Dec 6 '17 at 22:34
• @amoeba: Thank you for your comment. In the linked thread, there is a full explanation for the "random effects" part. That is the focus of the thread. They also say something about "fixed effects", but more in a mathematically way. So for me, the difference in case of fixed effects is not clear to me. It is especially not explained in simple word. – Olaf_SQL Dec 6 '17 at 23:04
• But it's exactly the same as in econometrics: as you said, "dummy variable for each individual is introduced". Maybe this thread stats.stackexchange.com/questions/4700 can also help you (see the second answer). – amoeba Dec 6 '17 at 23:12
• @amoeba: In my opinion, that cannot be true. I found examples for mixed models where the "fixed effect" was a continuous variable. That does not make sense to me to introduce dummy variables for this variable. Meanwhile I found this explanation: "The fixed effects are analogous to standard regression coefficients and are estimated directly." This would be more logic to me. What do think about this? – Olaf_SQL Dec 7 '17 at 8:44
• In mixed models, fixed effect is what you have in usual regression. If it's continuous variable, then it's one regression coefficient. If it's a categorical variable, then it's a separate regression coefficient for each dummy variable. – amoeba Dec 7 '17 at 8:52