Specifying Crossed vs. Nested Factors with Lmer and bootstrapping downstream statistics

andydolman at gmail.com


2009/9/9 <ledonret at email.unc.edu>

Dear List,

I have been using R for a couple of years now, but I am very new to the
lme4 package. I am currently trying to use lmer to analyze a mixed model,
and also trying to bootstrap some downstream statistics that utilize the
variance components I am obtaining from this model. However, I'm not sure
that I am specifying the model correctly, and while I have written a
function that works with the boot package for iterations of up to about 30,
it will not work for greater iterations. I was hoping you or others could
shed some light on these issues!

*I am using lme4 version 0.99375-28 with Mac OS X version 10.5.7

My design is this: I created 9 Families, and I treated these families with
two diets. Each family by diet combination was replicated 9 times
(randomized and interspersed). In my model, I am treating Family as a random
effect, and Diet as a fixed effect. I am mostly concerned with determining
the variance of the Family by Diet interaction. From previous queries, I
gathered that the correct specification would be this (disregarding
replicate)

lmer(SVL ~ Treatment + (1|Family) + (1|Family:Treatment), dataset)

or equivalently

lmer(SVL ~ Treatment + (1|Family/Treatment), dataset)

where "SVL" is my trait. It's a little confusing to me, because in the
second formula it appears that Treatment is nested in Family, instead of
being completely crossed with family, but I tried both ways and they gave me
the same answer, so I was satisfied.

Both these specifications are for nested models, for crossed you want

lmer(SVL ~ Treatment + (1|Family) + (1|Treatment), dataset)


But you've only got 2 levels of Treatment so it's probably not suitable to
treat it as random, particularly as you want to use the variance components.

However, I'd also like to add replicate (Box1) as a nested factor. The way
I'd intuitively write that,

lmer(SVL ~ Treatment + (1|Family/Treatment/Box1), dataset)

should mean that replicate is completely cross with Family, instead of
being nested within. The way I tried to deal with this was to make sure each
replicate had a unique identity... is that sufficient?

To nest Box in e.g. Treatment you'd do

lmer(SVL ~ Treatment + (1|Family) + (1|Treatment/Box1), dataset)

if that's what you want to do.

My second issue concerned bootstrapping and some errors that I receive when
trying to use this with an R>30. The function that I am attempting to use is
a function that I wrote to calculate heritability (I am trying to bootstrap
my estimate of the heritability of the Diet by Treatment interaction).

#The function

fun<-function(data,i){

+ d<-data[i,]
+ M<-lmer(SVL~Treatment+(1|Family/Box1/Family),d)

family is nested in family here - probably not at all what you want

+ Mv<-VarCorr(M)
+ varcomps<-c(unlist(lapply(Mv,diag))) #Variance of random factors
+ resid<-(attr(Mv,"sc")^2) #Residual Variance
+ VarTot<-sum(varcomps,resid) #Total variance
+ VarFamTrt<-Mv$`Treatment:Family`[1,1] #Variance for Family by Treatment
+ return((2*VarFamTrt)/VarTot)} #Heritability
#bootstrapping

Fam.boot<-boot(data,statistic=fun,R=10)

This will work up to about R=30, but beyond that, I get this error message,

Warning message:
In mer_finalize(ans) : singular convergence (7)

I realize this is probably a problem that isn't specific to lmer, but it is
the first time that I have run into it, so I'm at a loss for what to do.

Thank you so much in advance, for any insight you can provide!

Best, Cristina Ledon-Rettig
UNC-Chapel Hill

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