[R-sig-ME] A graphic for Random intercepts via distributions
Simon Harmel
@|m@h@rme| @end|ng |rom gm@||@com
Thu Jul 9 01:49:04 CEST 2020
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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