[R-sig-ME] zero variance query

[Ben Bolker]

Emmanuel Charpentier wrote:
> Le lundi 01 juin 2009 à 18:00 +0100, Christine Griffiths a écrit :
>> 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?
> 
> Hmmm... IST vaguely R that, when the world was young and I was (already)
> silly, Poisson distribution used to be a *discrete* distribution. Of
> course, this may or may not stand for "quasi"Poisson (for some value of
> "quasi").
> 
> May I inquire if you tried to analyze log(Abundance) (or log(Count),
> maybe including log(area) in the model) ?
> 
> HTH,
> 
> 					Emmanuel Charpentier
> 
>> 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?

   I think so ...

>> 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?

  To agree with what Emmanuel said above: you should use Count~...,
offset=log(area) for the correct analysis ...  that should solve
both your technical (zero random effects) and conceptual (even
quasiPoisson should be discrete data) issues.

>>
>>> 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
>>
> 
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-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / www.zoology.ufl.edu/bolker
GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc