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

[Ben Bolker]

   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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