[R-sig-ME] zero variance query
Christine Griffiths
Christine.Griffiths at bristol.ac.uk
Tue Jun 2 11:45:40 CEST 2009
Dear Emmanuel and Ben
Many thanks for your advice. Unfortunately, I don't think that I can offset
with log(area), given that each area is the same. My rationale for
converting to m2 was to standardise abundances to 1 m2 as I have other
parameters which were measured to different areas. I had previously
attempted to normalise my data by logging but felt that it did not improve
the distribution. I just hadn't tried it in my modelling. Logging my count
data dramatically improved the fit of the model (AIC 116.7 v 312.5),
however the variance still remains low. Does this appear acceptable?
Furthermore, can I assess model fit of different transformations of the
same dataset using AIC values, i.e. compare log(Count) and inverse
transformed Count?
lncount<-log(Count+1)
m1<-m1<-lmer(lncount~Treatment+(1|Month)+(1|Block),family=quasipoisson)
summary(m1)
Generalized linear mixed model fit by the Laplace approximation
Formula: lncount ~ Treatment + (1 | Month) + (1 | Block)
AIC BIC logLik deviance
116.7 135.1 -52.33 104.7
Random effects:
Groups Name Variance Std.Dev.
Month (Intercept) 1.8937e-14 1.3761e-07
Block (Intercept) 3.5018e-02 1.8713e-01
Residual 3.9318e-01 6.2704e-01
Number of obs: 160, groups: Month, 10; Block, 6
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.4004 0.1239 -3.232
Treatment2.Radiata 0.4596 0.1305 3.522
Treatment3.Aldabra 0.4295 0.1334 3.220
Correlation of Fixed Effects:
(Intr) Trt2.R
Trtmnt2.Rdt -0.581
Trtmnt3.Ald -0.577 0.530
I used quasipoisson as my data is overdispersed. It was further improved by
an inverse transformation (AIC 43.54). Again I have small variances.
invcount<-1/(Count+1)
m3<-lmer(invcount~Treatment+(1|Month)+(1|Block),family=quasipoisson)
summary(m3)
Generalized linear mixed model fit by the Laplace approximation
Formula: invcount ~ Treatment + (1 | Month) + (1 | Block)
AIC BIC logLik deviance
43.54 62 -15.77 31.54
Random effects:
Groups Name Variance Std.Dev.
Month (Intercept) 0.0000000 0.000000
Block (Intercept) 0.0021038 0.045867
Residual 0.0926225 0.304339
Number of obs: 160, groups: Month, 10; Block, 6
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.51644 0.05411 -9.545
Treatment2.Radiata -0.36246 0.08401 -4.314
Treatment3.Aldabra -0.29319 0.08197 -3.577
Correlation of Fixed Effects:
(Intr) Trt2.R
Trtmnt2.Rdt -0.566
Trtmnt3.Ald -0.580 0.372
Log(Abundance) did not solve the problem of zero variance. If quasipoisson
errors are not acceptable to use with abundance, i.e. non-integers, is
there a family of errors that would be recommended? Or should I simply
multiply abundance to obtain whole numbers?
Many thanks in advance,
Christine
--On 01 June 2009 23:17 -0400 Ben Bolker <bolker at ufl.edu> wrote:
> 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
>>>
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>
> --
> 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
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
----------------------
Christine Griffiths
School of Biological Sciences
University of Bristol
Woodland Road
Bristol BS8 1UG
Tel: 0117 9287593
Fax 0117 925 7374
Christine.Griffiths at bristol.ac.uk
http://www.bio.bris.ac.uk/research/mammal/tortoises.html
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