Hi,

I was looking to ask a question about how one could specify and interpret
models in MCMCglmm when looking at the between-group variability in a
particular response variable which has been measured across different time
periods.

The examples I am working with at the moment come from studies in which we
have repeated measures of individuals behaviour both within a year and
across 3 years. One thing we were interested in was the consistency of the
behavioural response both within and between years So imagine we have
measured 10 individuals 10 different times across 3 years, giving us
10*10*3 = 300 total observations for a response variable y that is normally
distributed.

A relatively simple model might be:


mc1 <-MCMCglmm(y ~ as.factor(Year), random =~ Individual, data= Data)

however if I wanted to allow the between individual variance to vary by
year I could go:

mc2 <-MCMCglmm(y ~ as.factor(Year), random =~ us(as.factor(Year)):
Individual, data= Data)


Now, as I understand it the us structure allows me to estimate different
between individual variances for each year but it also gives me some
co-variances as well and it was these covariances that I wanted to be sure
about. Following the example from the blue tits analysis in chapter 3 of
the MCMCglmm course notes I thought that the covariances between different
years would give an indication of whether measurements from the same
individual but from different years were really independent. Could I then
use this covariance between years convert it to a correlation in order to
say whether individuals show a consistent response across years?

Alternatively you could maybe year as numeric and have a continuous random
slope approach and look at the correlation between intercept and slope?


mc2a <-MCMCglmm(y ~ as.numeric(Year), random =~ us(1+as.numeric(Year)):
Individual, data= Data)

although I find interpretation of the correlation between slopes and
intercepts tricky at times.


Also, for further extensions it'd be relatively straightforward to allow
the residual variance to differ across years as well


mc3 <-MCMCglmm(y ~ as.factor(Year), random =~ us(as.factor(Year)):
Individual, rcov=~idh(as.factor(Year)), data= Data)

but I wasn't sure whether you'd be able to extend to further to different
individuals

e.g

mc4 <-MCMCglmm(y ~ as.factor(Year), random =~ us(as.factor(Year)):
Individual, rcov=~idh(Individual), data= Data)

mainly due to a lack of samples per individual from which to estimate
variance?



Any help, advice or suggestions greatly appreciated.

Thanks

Ian

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