[R-sig-ME] Relationship between mixed-effects models and fixed-effects models

[James Pustejovsky]

I agree with Daneil's comments. Raudenbush has a very deep article on
generalizations of the de-meaning strategy:

Raudenbush, S. W. (2009). Adaptive centering with random effects: An
alternative to the fixed effects model for studying time-varying treatments
in school settings. *Education Finance and Policy*, *4*(4), 468-491.
https://cpb-us-w2.wpmucdn.com/voices.uchicago.edu/dist/6/1063/files/2018/11/AdaptiveCenterRandom-2009-educfinapoli.4.4.468.R-106edfh.pdf


On Mon, Jun 7, 2021 at 2:08 PM Daniel Lüdecke <d.luedecke using uke.de> wrote:

> I think FE (fixed effects) models are used in particular in panel data or
> longitudinal data analysis, when time varying predictors are included, e.g.
> "income". Income has a between-subject effect (we have higher- and
> lower-income groups) and a within-subject effect (income of person A can
> increase over time, while it can decrease for person B - no matter, if A or
> B belong to low- or high-income groups!).
>
> The arguments from a FE perspective against mixed models is that you cannot
> include "income" as predictor, because income has an effect on both
> individual level (within) and higher levels (between), i.e. it would
> introduce correlated error terms between the fixed effects and random
> effects, which violates model assumptions. The solution is now to "demean"
> the "income" variable and only include the within-effect, i.e. the time
> varying component in the model. All between effects, and in general all
> predictors that could be seen as "between" effects (gender, education, ...)
> have to be omitted from the model. The group-level variation (e.g.
> "subject", or whatever would be the group factor in mixed models) is
> included as normal predictor.
>
> So, a FE model is a classical linear model, where
> - Intercept is removed
> - time-invariant predictors are not allowed to be included
> - the group-level factor is included as predictor
> - time-varying predictors are de-meaned (“person-mean centered”, indicating
> the “within-subject” effect)
>
> However, in particular Bell et al. [1, 2] have shown that the "demeaning"
> trick also applies to mixed models, so that essentially, mixed models are
> probably much better for panel data / longitudinal data analysis. You may
> be
> interested in this vignette, describing the issue and comparing FE to mixed
> models: https://easystats.github.io/parameters/articles/demean.html
>
> There are some newer developments, like fixed effects individual slope
> models (package feisr), or the panelr package (fun fact: which uses lme4 to
> fit flexible models for panel data, so these models are actually mixed
> models, no classical FE models).
>
> Best
> Daniel
>
> 1) Bell, Andrew, Malcolm Fairbrother, and Kelvyn Jones. 2019. “Fixed and
> Random Effects Models: Making an Informed Choice.” Quality & Quantity 53:
> 1051–74. https://doi.org/10.1007/s11135-018-0802-x.
>
> 2) Bell, Andrew, and Kelvyn Jones. 2015. “Explaining Fixed Effects: Random
> Effects Modeling of Time-Series Cross-Sectional and Panel Data.” Political
> Science Research and Methods 3 (1): 133–53.
> https://doi.org/10.1017/psrm.2014.7.
>
> -----Ursprüngliche Nachricht-----
> Von: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> Im
> Auftrag von Douglas Bates
> Gesendet: Montag, 7. Juni 2021 17:10
> An: R-mixed models mailing list <r-sig-mixed-models using r-project.org>
> Betreff: [R-sig-ME] Relationship between mixed-effects models and
> fixed-effects models
>
> Occasionally I encounter discussions of what are called fixed-effects
> models in econometrics but I haven't seen descriptions of the underlying
> statistical model.  Can anyone point me to a description of these models,
> in particular a description in terms of a probability distribution of the
> response? I would be particularly interested in a discussion of how they
> relate to mixed-effects models as we think of them in lme4 and nlme.
>
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