#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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