Singular convergence in lmer

-----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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