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

[Simon Harmel]

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
> >
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> >
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