comparing random effect variation between data sets

Hi all

I have movement data for two species of fish (say species X and species Y).
The response variable is 'distance from home' (distance) and multiple
measurements (5-17) are made for 20-30 individuals per species over a
period of 200 days. Distance is continuous and strictly positive so I am
using a gamma distribution with a log link. My collegues would like me to
fit seperate models for each species to explore temporal patterns in
movement (time). We believe there will be non-linear patterns in movement
through time so have I have fitted GAMMs

I'm happy with the two models and their interpretation. I would, however,
like to compare the level of among-individual variation in movement between
species. The species-average trends are pretty similar but it looks like
there is more variance among individuals for species X than species Y.

I was thinking of extracting the individual level random effects from the
two models and performing a variance test on these. My logic is that given
the response variables are the same and the model structures are the same,
I could make a meaningful comparison of random effects. The overall model
intercepts are different but I thought this is not an issue here as I'm
only interested in the variance of the random effects, not their average.

Is this approach valid, or am I violating assumptions/ these data are not
directly comparable ? If not, what would be a potential way to perform this
comparision? Below is the code I'm thinking of using.

Thanks very much for your time

John

#####GAMMs
X1<-gamm4(distance ~ s(time,k=4), random=~(1|CODE),data=speciesX,
family=Gamma(link=log))
Y1<-gamm4(distance ~ s(time,k=4), random=~(1|CODE),data=speciesY,
family=Gamma(link=log))

######extract random effects from the two models
X1ranef<-ranef(X1$mer)###extract random effects from model
X1ranef<-data.frame(matrix(unlist(X1ranef$'CODE'),ncol=1))##convert list of
random effects to data frame
names(X1ranef)<-c('CODE')

Y1ranef<-ranef(X1$mer)###extract random effects from model
Y1ranef<-data.frame(matrix(unlist(Y1ranef$'CODE'),ncol=1))##convert list of
random effects to data frame
names(Y1ranef)<-c('CODE')

######perform variance test
var.test(X1ranef$CODE,Y1ranef$CODE)

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  A couple of quick thoughts:

* as a crude test, you could get the profile confidence intervals
for the random-effect SDs in each model and compare them
* a more formal test would put both species into the same model
and allow for different variances.  This might work:

library(lme4)
library(gamm4)
alldat <- rbind(data.frame(species="X",speciesX),
                data.frame(species="Y",speciesY))

comb <- gamm4(distance ~ s(time,k=4,by=species),
                  random=~(1|CODE)+(dummy(species,"Y")|CODE))

You could test of comb against the model with just random=~(1|CODE),
or look at the confidence intervals of the second RE term.


On Thu, Jun 25, 2015 at 9:07 AM, John Morrongiello
<jrmorrongiello at gmail.com> wrote:

Hi all

I have movement data for two species of fish (say species X and species

Y).

The response variable is 'distance from home' (distance) and multiple
measurements (5-17) are made for 20-30 individuals per species over a
period of 200 days. Distance is continuous and strictly positive so I am
using a gamma distribution with a log link. My collegues would like me to
fit seperate models for each species to explore temporal patterns in
movement (time). We believe there will be non-linear patterns in movement
through time so have I have fitted GAMMs

I'm happy with the two models and their interpretation. I would, however,
like to compare the level of among-individual variation in movement

between

species. The species-average trends are pretty similar but it looks like
there is more variance among individuals for species X than species Y.

I was thinking of extracting the individual level random effects from the
two models and performing a variance test on these. My logic is that

given

the response variables are the same and the model structures are the

same,

I could make a meaningful comparison of random effects. The overall model
intercepts are different but I thought this is not an issue here as I'm
only interested in the variance of the random effects, not their average.

Is this approach valid, or am I violating assumptions/ these data are not
directly comparable ? If not, what would be a potential way to perform

this

comparision? Below is the code I'm thinking of using.

Thanks very much for your time

John

#####GAMMs
X1<-gamm4(distance ~ s(time,k=4), random=~(1|CODE),data=speciesX,
family=Gamma(link=log))
Y1<-gamm4(distance ~ s(time,k=4), random=~(1|CODE),data=speciesY,
family=Gamma(link=log))

######extract random effects from the two models
X1ranef<-ranef(X1$mer)###extract random effects from model
X1ranef<-data.frame(matrix(unlist(X1ranef$'CODE'),ncol=1))##convert list

of

random effects to data frame
names(X1ranef)<-c('CODE')

Y1ranef<-ranef(X1$mer)###extract random effects from model
Y1ranef<-data.frame(matrix(unlist(Y1ranef$'CODE'),ncol=1))##convert list

of

random effects to data frame
names(Y1ranef)<-c('CODE')

######perform variance test
var.test(X1ranef$CODE,Y1ranef$CODE)

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