zero variance query
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 ? 18:00 +0100, Christine Griffiths a ?crit :
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
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---------------------- 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