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correlation between random effects

2 messages · Jana Dlouha, Thierry Onkelinx

Original
Jana Dlouha
# 
Hi all,

I have a problem with a correlation between random effects. I have tested several models on my data:
m0<-lm(MCs~ dB1, data)
m1<- lmer(MCs~ dB1 + (1|Species), data, REML=FALSE)
m2 <- lmer(MCs~ dB1 + (-1+dB1|Species), data, REML=FALSE)
m3<- lmer(MCs~ dB1 + (1|Species)+(0+dB1|Species), data, REML=FALSE)
m4<- lmer(MCs ~ dB1 + (1+dB1 |Species), data,REML=FALSE)

and when I compare the AIC criterion, the lowest one is for the model m4:
     m0              m1           m2            m3            m4
11086.51 10948.72 10828.75 10830.75 10720.43

However, in the summary I see that there is a strong correlation between random effects and associated variances are huge:
Random effects:
Groups   Name        Variance Std.Dev. Corr
 Species  (Intercept) 21.48    4.635
          dB1         11.25    3.355    -1.00
Residual              6.19    2.488
Number of obs: 2221, groups:  Species, 598

For m3, random effect associated with  intercept has very low variance and residual variance is only  a bit higher:
Random effects:
Groups    Name        Variance  Std.Dev.
 Species   (Intercept) 3.419e-14 1.849e-07
Species.1 dB1         7.968e-01 8.927e-01
Residual              6.327e+00 2.515e+00
Number of obs: 2221, groups:  Species, 598

I am tempted to take into account only the randon effect associated with the slope however I don't know if i can do this considering that the AIC is not the lowest one for this model and how to justify it in my paper?
By the way, I don't really understand why the variances associated with the random effects change so much.
I have tried to center the regressor dB1 which removed the correlation between fixed effects and changed the sign of correlation but random effects remain strongly correlated and variances large:

Random effects:
Groups   Name        Variance Std.Dev. Corr
Species  (Intercept)  1.109   1.053
          dB1c        11.255   3.355    0.94
Residual              6.190   2.488
Number of obs: 2221, groups:  Species, 598

Could you please give me some hint to solve my problem? Thanks a lot in advance

Jana
Thierry Onkelinx
# 
Dear Jana,

I assume that you uses the centered dB1c both in the random and the
fixed effects? Another thing you can try is to scale dB1c. Using
sensible units is often sufficient. Don't use large units (e.g.
kilometers) when you are measuring small things (e.g. millimeters).

You'll need to provide more information when you need more feedback.
At least the summary of the data and the model.

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

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2018-02-13 10:00 GMT+01:00 Jana Dlouha <jana.dlouha at inra.fr>: