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

[Simon Harmel]

Javier,

These pictures were made by a friend of mine. Feel free to use them for
your classes. However, I wonder, how would you guys change the graphs I
shared here to represent a cross-classified (crossed-design), roughly
speaking?

Simon

On Thu, Jul 9, 2020 at 12:19 AM Javier Seoane <javier.seoane using uam.es> wrote:

> 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]]
>> > >> >
>> > >> > _______________________________________________
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>> > >>
>> > >> _______________________________________________
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>> >
>>
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>
>
> --
>
> = = = = = = = = = = = = = = = = = = = =
>
>
> 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
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>

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