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

[Simon Harmel]

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
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> thierry.onkelinx using inbo.be
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>
>
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>
> 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]]
>>
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>

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