[R-sig-ME] Singular convergence in lmer

[ONKELINX, Thierry]

Dear Benjamin,

It is not clear to me how your M1 model will capture the effect of the fish, unless via the combined effects of year, site, ... That is IMHO overly complex.

If you have only a few levels, you can run into numerical problems. Therefore I avoid using variables with a low number of levels as random effect. If they are important, then I add them as fixed effects. I prefer 2 or 3 parameter estimates of fixed effects instead of 1 dodgy variance estimate. Note that the overall difference in degrees of freedom is small. 
6 or 7 levels is doable, but still rather low. Maybe you should use only the interaction between year and site as random effects in which you can nest (or cross?) the effect of the fish.

Best regards,

Thierry

> -----Oorspronkelijk bericht-----
> Van: Benjamin J. Ciotti [mailto:ciotti at UDel.Edu]
> Verzonden: maandag 3 oktober 2011 14:47
> Aan: ONKELINX, Thierry; r-sig-mixed-models at r-project.org
> Onderwerp: RE: [R-sig-ME] Singular convergence in lmer
> 
> Dear Thierry,
> 
> Thank you for your response. If you look carefully at the data structure and M1,
> fish is in fact a random effect (residual error variance) in the original model. I
> considered including year as a fixed effect for the reason you mentioned, but
> others have suggested that the number of levels shouldn't influence whether a
> factor is fixed or random. Maybe I should reconsider?
> Site actually has 7 levels in the 'real' dataset - enough to estimate variance
> according to Zuur et al.'s criteria.
> 
> Thanks again for your input.
> 
> Ben
> 
> -----Original Message-----
> From: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
> Sent: Monday, October 03, 2011 5:52 AM
> To: Benjamin J. Ciotti; r-sig-mixed-models at r-project.org
> Subject: RE: [R-sig-ME] Singular convergence in lmer
> 
> Dear Benjamin,
> 
> I think you will need to do some reading on mixed models. I would suggest Zuur
> et al (2009)
> 
> @BOOK{
>   title = {Mixed Effects Models and Extensions in Ecology with R},
>   publisher = {Springer New York},
>   year = {2009},
>   author = {Zuur, Alain F. and Ieno, Elena N. and Walker, Neil J. and Saveliev,
> 	Anatoly A. and Smith, Graham M.},
>   doi = {10.1007/978-0-387-87458-6},
> }
> 
> I would expect to see fish as a random effect in your model. Further you have
> too few levels of year and site to get a reliable estimate of the variance. Hence
> a more sensible model would be something like:
> 
> lmer(G~ Day * Year * Site + (1|Fish),REML=TRUE,data=GData)
> 
> Best regards,
> 
> Thierry
> 
> 
> > -----Oorspronkelijk bericht-----
> > Van: r-sig-mixed-models-bounces at r-project.org
> > [mailto:r-sig-mixed-models- bounces at r-project.org] Namens Benjamin J.
> > Ciotti
> > Verzonden: maandag 3 oktober 2011 1:02
> > Aan: r-sig-mixed-models at r-project.org
> > Onderwerp: [R-sig-ME] Singular convergence in lmer
> >
> > #Dear All,
> >
> >
> >
> > #I have measured growth rate (G, response variable) in 10 individual
> > fish
> > (Fish) on 5 dates (Days, fixed covariate) at 4 sites (Site) in each of
> > 2
> years (Year).
> >
> > #An example data set, using random numbers for the response, is GData,
> > as
> > follows:
> >
> >
> >
> > set.seed(14)
> >
> > Year<-as.factor(sort(rep(c(2005,2007),400)))
> >
> > Site<-as.factor(rep(sort(rep(c("a","b","c","d"),50)),4))
> >
> > Year.Site<-as.factor(paste(Year,Site,sep="."))
> >
> > Day<-as.numeric(rep(sort(rep(c(1,15,30,45,60),10)),16))
> >
> > Fish<-as.factor(rep(seq(1,10),80))
> >
> > G<-rnorm(800,0.05,0.025)
> >
> > GData<-data.frame(Year,Site,Year.Site,Day,Fish,G)
> >
> > #I am modelling the temporal trend in growth rate as a linear function
> > of
> Day,
> > the slope and intercept of which can vary as a random function of
> > Year,
> Site and
> > Year.Site.
> >
> > library(lme4)
> >
> > M1<-
> > lmer(G~Day+(1|Year)+(1|Site)+(0+Day|Year)+(1|Year.Site)+(0+Day|Site)+(
> > 0+
> > Day|Year.Site),REML=TRUE,data=GData)
> >
> >
> >
> > #You will note that there is singular convergence (with this, but not
> > all,
> random
> > number seeds).
> >
> > #Does this necessarily mean that there is a fundamental flaw in the
> > model design, or does it just mean that with this data set, a simpler
> > model is
> necessary?
> >
> >
> >
> > #In the real data set, all random terms except Year.Site and the
> interaction
> > between Day and Year.Site can be dropped without substantial changes
> > in
> AIC.
> >
> > #I therefore conclude that the following model is sufficient to
> > describe
> the
> > spatial and temporal growth variation:
> >
> > M2<-lmer(G~Day+(1|Year.Site)+(0+Day|Year.Site),REML=TRUE,data=GData)
> >
> >
> >
> > #My question is whether the initially model is fundamentally flawed,
> > or
> whether
> > it just needs to be simplified?
> >
> > #For example, is it valid to compare the full model with simpler
> > models,
> even
> > though it converged to singularity?
> >
> >
> >
> > #Any advice would be greatly appreciated.
> >
> >
> >
> > Benjamin J. Ciotti
> >
> > University of Delaware
> >
> >
> >
> >
> > 	[[alternative HTML version deleted]]
> >
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