[R-sig-ME] Meaning of Corr of random-effects with a cross-level interaction

[Thierry Onkelinx]

Dear Simon,

The plot shows a set of dots on a vertical line indicating an upper bound
on ses. The few points outside the bound need investigating in a real
dataset. They might be wrong measurements.

If you have a response variable with a boundary, you need to use a
distribution that copes with that. Using a Gaussian distribution with
please of data close to a boundary, might lead to predictions and
confidence intervals outside of the boundary. I've seen people give a talk
on mortality with confidence intervals like (80%; 120%)...

I've no idea WHY you are getting the false convergence, just WHEN it starts
to kick in.

If you are cross posting you question, please do mention that.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
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<https://www.inbo.be>


Op vr 25 sep. 2020 om 19:35 schreef Simon Harmel <sim.harmel using gmail.com>:

> Thank you Thierry! Would you please clarify one of your sentences: "both
> math and ses have bounds. Ses even seems to have some data above its
> upper bound."
>
> Specifically, would please clarify what you mean by "ses has some data
> above its upper bound"?(you mean the couple of outlying ses values in red
> as shown in your plot?)
>
> Of course, real world data always have some lower and upper bound based on
> the instrument (e.g., a math test) used to collect the data. But my
> question is what are the relative required lower and upper bounds on
> NUMERIC OUTCOME & NUMERIC PREDICTORS so we don't face convergence issues
> of the type I have shown in my question?
>
> Thank you,
> Simon
>
> On Fri, Sep 25, 2020 at 3:03 AM Thierry Onkelinx <thierry.onkelinx using inbo.be>
> wrote:
>
>> Dear Simon,
>>
>> A perfect correlation between random effect parameters indicates a
>> problem. Note the failed convergence warning.
>> Standardising ses makes things even worse: it yields a singular fit error.
>>
>> Removing the random slope of ses or the sector interaction solves the
>> problem. i.e. the model runs and yields sensible output.
>>
>> Looking at the data, it seems like both math and ses have bounds. Ses
>> even seems to have some data above its upper bound.
>> The model assumes no bounds in the response variable. Maybe this is the
>> cause of the problem.
>>
>> ggplot(hsb, aes(x = ses, y = math, colour = factor(sector))) +
>>   geom_point()
>>
>> Best regards,
>>
>> Thierry
>>
>>
>> ir. Thierry Onkelinx
>> Statisticus / Statistician
>>
>> Vlaamse Overheid / Government of Flanders
>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
>> AND FOREST
>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>> thierry.onkelinx using inbo.be
>> Havenlaan 88 bus 73, 1000 Brussel
>> www.inbo.be
>>
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
>> The combination of some data and an aching desire for an answer does not
>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>>
>> <https://www.inbo.be>
>>
>>
>> Op do 24 sep. 2020 om 18:39 schreef Simon Harmel <sim.harmel using gmail.com>:
>>
>>> Dear All,
>>>
>>> I had a quick question. I have a cross-level interaction in my model
>>> below
>>> (ses*sector). My cluster-level predictor "sector" is a binary variable
>>> (0=Public, 1=Private). My level-1 predictor is numeric.
>>>
>>> QUESTION:  The `Corr = 1` is indicating the correlation between
>>> intercepts and slopes across BOTH public & private sectors (like their
>>> average) OR something else?
>>>
>>> hsb <- read.csv('
>>> https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')
>>>
>>> summary(lmer(math ~ ses*sector + (ses|sch.id), data = hsb))
>>>
>>>
>>> Random effects:
>>>  Groups   Name        Variance Std.Dev.     Corr
>>>  sch.id   (Intercept)  3.82107    1.9548
>>>           ses                0.07587     0.2754        1.00
>>>  Residual             36.78760 6.0653
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models using r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>

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