[R-sig-ME] correlation between random effects

[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



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