[R-sig-ME] A graphic for Random intercepts via distributions

[Javier Seoane]

Simon, will you have those pictures available somewhere for educational
purposes? My field is ecology, where mixed models are more often presented
otherwise, not stressing that hierarchy among levels so much as in
education studies. However, I find the pictures could be useful to my
students,  along with the caveats you and Ben Bolker have made.





El jue., 9 jul. 2020 a las 2:11, Simon Harmel (<sim.harmel using gmail.com>)
escribió:

> Thanks so much, will do all that!
>
> On Wed, Jul 8, 2020 at 6:45 PM Ben Bolker <bbolker using gmail.com> wrote:
>
> >    I agree that the second version you link to might be slightly more
> > technically correct, but I don't think there's anything about harmful.
> >    The most important correction (IMO) would be to make the red
> > (level-2) distribution much wider, so that it actually matched the
> > scale of the level-1 distribution.  (The other problem with the
> > picture is that for prettiness, the beta_{0x} values we can see appear
> > evenly spaced, which is unrealistic ...)
> >
> > On Wed, Jul 8, 2020 at 7:25 PM Simon Harmel <sim.harmel using gmail.com>
> wrote:
> > >
> > > Thanks Ben. The notations e_{ij} for the residual error of individual i
> > in school j and U_{0j} for the deviation of school j's mean from the
> grand
> > mean is just how educational methodologists denote these concepts.
> > >
> > >  But specifically, I thought regression concepts like e_{ij} and U_{0j}
> > all should be correctly shown on a scatter plot like this:
> > https://github.com/hkil/m/blob/master/mlm2.PNG.
> > >
> > > So, with your suggestions is this a better picture?:
> > https://github.com/hkil/m/blob/master/mlm3.PNG
> > >
> > > Is there a relationship between the scale of the fist-level
> > distributions, and the second-level distribution that the picture should
> > observe?
> > >
> > > Thanks,
> > > Simon
> > >
> > >
> > > On Wed, Jul 8, 2020 at 5:51 PM Ben Bolker <bbolker using gmail.com> wrote:
> > >>
> > >>      Can you clarify your concern?
> > >>
> > >> I can see things to quibble about here (the scales of the level-2 and
> > >> level-1 diagrams are different; I don't know why they're using e_{ij}
> > >> for the residual error of individual i in school j but U_{0j} for the
> > >> deviation of school j around the grand mean; it's a little confusing
> to
> > >> have "level 1" above "level 2" in the text but level 2 above level 1
> in
> > >> the picture; it's potentially confusing for the arrow showing the
> > >> deviation from the baseline to intersect with the population density
> > >> curve [technically, the deviation doesn't have a "level", so could be
> > >> drawn instead as an arrow between two vertical lines rather than from
> a
> > >> line to a particular point ...
> > >>
> > >> ... but nothing that seems actively misleading.
> > >>
> > >>    Others may have other opinions or see something I'm missing.
> > >>
> > >> On 7/8/20 6:27 PM, Simon Harmel wrote:
> > >> > Good afternoon,
> > >> >
> > >> > I came across a picture (
> > https://github.com/hkil/m/blob/master/mlm.PNG)
> > >> > that tries to show the concept of random-intercept models using
> > >> > distributions.
> > >> >
> > >> > I think, however, the picture erroneously mixes regression concepts
> > (e.g.,
> > >> > error terms) with distributional properties of those regression
> > concepts.
> > >> >
> > >> > I appreciate confirmation from the expert members?
> > >> >
> > >> > Thanks,
> > >> > Simon
> > >> >
> > >> >       [[alternative HTML version deleted]]
> > >> >
> > >> > _______________________________________________
> > >> > R-sig-mixed-models using r-project.org mailing list
> > >> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> > >>
> > >> _______________________________________________
> > >> R-sig-mixed-models using r-project.org mailing list
> > >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-models using r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>


-- 

= = = = = = = = = = = = = = = = = = = =


Javier Seoane Pinilla
Profesor Titular
Centro de Investigación en Biodiversidad y Cambio Global (CIBC-UAM)
Departamento de Ecologia
Universidad Autonoma de Madrid
Edificio de Biología
Darwin, 2
E-28049 Madrid
SPAIN

e-mail: javier.seoane using uam.es
webpage: http://teguam.es/miembros/javier-seoane/
Tlf: +34 91 497 3639
= = = = = = = = = = = = = = = = = = = =

	[[alternative HTML version deleted]]