[R-sig-ME] Trend in total number of animals

[Jarrod Hadfield]

Dear Thierry,

I THINK the fixed effect slope should be what you're after if you want  
to predict the change in log numbers, but simply exponentiating the  
prediction will not give you a true measure of the arithmetic increase.

The arithmetic prediction for years 1:10 (for example) when the slope  
variance for the year|room term is zero would be:

exp(b_year*1:10+0.5*(v1+v2))

where b_year is your slope estimate, and v1 is the year intercept  
variance and v2 is the room intercept variance.

When slope variance exists this becomes more difficult, because it  
implies the variance v2 changes as a function of year. In this case:

v2=diag(Z%*%V2%*%t(Z))

where

Z<-cbind(rep(1,10), 1:10)

and V2 is the covariance matrix of the room intercept-slopes.

Or if you like

v2 = V2[1,1]+(1:10)*V2[1,2]*2+(1:10^2)*V2[2,2]

Another difficulty is the possibility that your missing data are not  
"completely missing at random". By default lmer just seems to omit  
missing data rather than dealing with it properly, but perhaps there  
is an argument that can be passed to na.omit which suppresses this? If  
so, then the less strict assumption of "missing at random" can be  
made. In this latter case the missing data only have to be random  
conditional on the observed data - for example, if there were no bats  
in room A in year 1 which made the field workers less inclined to  
visit room A in year 2 based on their knowledge of the 1'st year's  
count.

Cheers,

Jarrod

Quoting "ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be>:

> Dear all,
>
> We are modelling the total numbers of hibarnating bats in a fortress. We
> have data of the number of bats per room spanning ten years. The main
> problem is that not all rooms were visited each year. The fieldworkers
> did not known or find all rooms and some rooms were not allways
> accessible.
>
> Some of the rooms were not counted in the early years and they contain a
> rather high number of bats in the more recent years. So a glm on the
> total observed number would be very biased. Therefore we would use a
> mixed model on the numbers of bats per room. The model looks like:
> glmer(Number ~ Year + (1|Year) + (Year|Room), family = poisson). Year is
> the long-term trend. (1|Year) allows for year-to-year variability (due
> to weatherconditions) and (Year|Room) allows for a random intercept and
> slope per room.
>
> Our main question about this model is the interpretation of the
> long-term trend (fixed effect of Year). Given the model specification it
> is the trend in an 'average' room from the population of rooms. Can we
> assume that this trend equals the trend in the total number of bats in
> the fortress. That would be the trend in to total observed numbers if we
> could have investigated every room in every year.
> Or is it better to use the model to simulate the total number of bats
> and then model this simulated totals using a simple glm? Repeating the
> simulations a large number of times would yield an average and
> confidence intervals for the trend.
>
> Best regards,
>
> Thierry
>
> ------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek
> team Biometrie & Kwaliteitszorg
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> Research Institute for Nature and Forest
> team Biometrics & Quality Assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
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