Singular convergence in lmer

 others have suggested that the number of levels shouldn't influence whether a factor is fixed or random.

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




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