Meaning of Corr of random-effects with a cross-level interaction

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 at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op do 24 sep. 2020 om 18:39 schreef Simon Harmel <sim.harmel at 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

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