Dear Christine,
"Logging my count data dramatically improved the fit of the model (AIC 116.7
v 312.5),"
Don't be mislead by reductions in AIC after transforming your response
variable. You can't use AIC to compare models with different response
variables - even if they are just transformations of each other.
The low variance you get for your random effects just indicates that there
is not much difference between months and blocks in your data - I think.
But you are best sticking to the raw counts if you want to use Poisson. As
Ben says, just re-scale the estimated parameters to units per metre - or use
an offset if your areas are not constant.
Andy.
andydolman@gmail.com
2009/6/2 Ben Bolker
> Christine Griffiths wrote:
> > 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.
>
> Why not? All the offset does is add a constant (i.e., fixed rather
> than estimated -- could be the same or different for different
> observations) to the regression model.
>
> > My rationale for
> > converting to m2 was to standardise abundances to 1 m2 as I have other
> > parameters which were measured to different areas.
>
> Don't quite understand this. Parameters from other studies that you
> want to compare in discussion? If so, you can just rescale your
> predictions/parameters *after* you estimate them ...
>
> 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?
>
> No, not without a correction. See
>
> http://www.unc.edu/courses/2007spring/enst/562/001/docs/lectures/lecture22.htm
>
> Generalized linear modeling is not as flexible (in some ways) as
> classical linear models -- you can't just transform the data any way you
> want (in principle I suppose you could, but it's basically not possible
> to "transform to achieve a Poisson distribution" the way you would
> transform continuous data to achieve normality etc.)
>
> >
> > 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 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@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@ufl.edu / www.zoology.ufl.edu/bolker
> >> GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc
> >>
> >> _______________________________________________
> >> R-sig-mixed-models@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@bristol.ac.uk
> > http://www.bio.bris.ac.uk/research/mammal/tortoises.html
>
>
> --
> Ben Bolker
> Associate professor, Biology Dep't, Univ. of Florida
> bolker@ufl.edu / www.zoology.ufl.edu/bolker
> GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc
>
> _______________________________________________
> R-sig-mixed-models@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
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