# interpretation of random effects in GLMM

I want to look at Spatial variation of juvenile density.I want to see variation both within and between sites. I would like some help in interpretation of within site variation part. My study design is like this: I have 5 sites, 2 subsites within each site and 2 permanent quadrates within each site. So I have 5 sites, 10 subsites and 20 quadrats. I have done implicit nesting, i.e. sites, subsites and quadrats are uniquely named. My Data-set structure looks like this:

 Site Subsite juv.n Quadrat 1 Hamamoto Hamamoto I 6 190 2 Hamamoto Hamamoto I 1 196 3 Hamamoto Hamamoto II 7 187 4 Hamamoto Hamamoto II 0 189 5 S.Station S.station I 6 147 6 S.Station S.station I 12 149 

Since my data does not have homogenous variance nor follow normal distribution, I did GLMM with Poisson distribution in R. I ran the following code.

 Msite <- glmer(juv.n ~ Site + (1|Subsite) + (1|Quadrat), family = poisson(link = "log"), data = Jdensity1) 

And I got following summary

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod]
Family: poisson  ( log )
Formula: juv.n ~ Site + (1 | Subsite) + (1 | Quadrat)
Data: Jdensity1

AIC      BIC   logLik deviance df.resid
146.8    153.7    -66.4    132.8       13

Scaled residuals:
Min      1Q  Median      3Q     Max
-1.5254 -0.4356  0.2294  0.3192  1.1640

Random effects:
Groups  Name        Variance  Std.Dev.
Quadrat (Intercept) 1.384e-01 3.721e-01
Subsite (Intercept) 3.673e-10 1.916e-05
Number of obs: 20, groups:  Quadrat, 20; Subsite, 10

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)        1.1667     0.3315   3.519 0.000432 ***
SiteS.Station      1.1422     0.4095   2.789 0.005288 **
SiteSouth Sesoko   0.6977     0.4251   1.641 0.100756
SiteWest Sesoko    2.8433     0.3856   7.374 1.65e-13 ***
SiteYakke Reef     2.2699     0.3890   5.835 5.37e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) StS.St StSthS StWstS
SiteS.Statn -0.805
SiteSothSsk -0.775  0.625
SiteWestSsk -0.858  0.691  0.665
SiteYakkRef -0.844  0.681  0.656  0.724


I can understand the fixed effect part. For random effects I can see that both subsites and quadrats have variance close to zero. Am I correct in assuming that variation within sites is close to zero, i.e. there is close to 0 variation between, Hamamoto I and Hamamoto II ? Is there a way to get Probability values of the random factor ? The variance of subsite : Is that the value of variance between subsites at one site or variance between all subsites (at all sites)?

• Are you sure that explicitly nesting is not more appropriate here? A crossed random effect like (1|Subsite) + (1|Quadrat) is plausible but actually it seems you have 2 quadrats within each subsite (otherwise how can they be 20 if you have only 5 sites and 2 quadrates within each site). In that case (1|Subsite/Quadrat) might be more appropriate. – usεr11852 Apr 22 '17 at 23:19