[R-sig-ME] zero variance query

[Christine Griffiths]

Dear R users,

I am having a problem with getting zero variance in my lmer models which 
specify two random effects. Having scoured the help lists, I have read that 
this could be because my variables are strongly correlated. However, when I 
simplify my model I still encounter the same problem.

My response variable is abundance which ranges from 0-0.14.

Below is an example of my model:
> m1<-lmer(Abundance~Treatment+(1|Month)+(1|Block),family=quasipoisson)
> summary(m1)
Generalized linear mixed model fit by the Laplace approximation
Formula: Abundance ~ Treatment + (1 | Month) + (1 | Block)
   AIC   BIC logLik deviance
 17.55 36.00 -2.777    5.554
Random effects:
 Groups   Name        Variance   Std.Dev.
 Month    (Intercept) 5.1704e-17 7.1906e-09
 Block    (Intercept) 0.0000e+00 0.0000e+00
 Residual             1.0695e-03 3.2704e-02
Number of obs: 160, groups: Month, 10; Block, 6

Fixed effects:
                   Estimate Std. Error t value
(Intercept)        -3.73144    0.02728 -136.80
Treatment2.Radiata  0.58779    0.03521   16.69
Treatment3.Aldabra  0.47269    0.03606   13.11

Correlation of Fixed Effects:
            (Intr) Trt2.R
Trtmnt2.Rdt -0.775
Trtmnt3.Ald -0.756  0.586

1. Is it wrong to treat this as count data?
2. I would like to retain these as random factors given that I designed my 
experiment as a randomised block design and repeated measures, albeit 
non-orthogonal and unbalanced. Is it acceptable to retain these random 
factors, is all else is correct?
3. The above response variable was calculated per m2 by dividing the Count 
by the sample area. When I used the Count (range 0-9) as my response 
variable, I get a small but reasonable variation of random effects. Could 
anyone explain why this occurs and whether one response variable is better 
than another?

> m2<-lmer(Count~Treatment+(1|Month)+(1|Block),family=quasipoisson)
> summary(m2)
Generalized linear mixed model fit by the Laplace approximation
Formula: Count ~ Treatment + (1 | Month) + (1 | Block)
   AIC BIC logLik deviance
 312.5 331 -150.3    300.5
Random effects:
 Groups   Name        Variance Std.Dev.
 Month    (Intercept) 0.14591  0.38198
 Block    (Intercept) 0.58690  0.76609
 Residual             2.79816  1.67277
Number of obs: 160, groups: Month, 10; Block, 6

Fixed effects:
                   Estimate Std. Error t value
(Intercept)          0.3098     0.3799  0.8155
Treatment2.Radiata   0.5879     0.2299  2.5575
Treatment3.Aldabra   0.5745     0.2382  2.4117

Correlation of Fixed Effects:
            (Intr) Trt2.R
Trtmnt2.Rdt -0.347
Trtmnt3.Ald -0.348  0.536

Many thanks,
Christine