[R-sig-ME] MCMCglmm - ZIP model for mackerel egg data

[Jarrod Hadfield]

Hi Sven,

Quoting "Gastauer, Sven" <sven.gastauer at wur.nl> on Thu, 7 Feb 2013  
16:11:49 +0000:

> Dear all,
>
> I am trying to model mackerel egg abundance in the North Sea. The  
> egg abundance information comes from triennial surveys and contains  
> a lot of 0 values (e.g. samples without any mackerel eggs). The idea  
> was hence to build a zero-inflated or a zero-altered model using  
> MCMCglmm. Fixed terms should be Sea Surface Temperature (sst),  
> Longitude, Latitude and years as random factor.
>
> The first problem or question I ran into is that of course the  
> number of eggs within a sample is a simple integer, although  
> normally I would define an offset : Egg abundance = Counted Eggs x  
> Correction Factor x Sampling Depth / Filtered Volume  
> (Ce*R*SD/VolFilt), but as far as I understand it this is not an  
> option in MCMCglmm? My easy solution for now was to simply round  
> volume the corrected  egg counts, which introduces a minor error.

You can fit an offset by fixing the regression coefficient at 1 in the  
prior. For example if the offset variable is associated with the 2nd  
fixed effect out of 3 then:

prior<-list(B=list(V=diag(3)*1e+8, mu=c(0,1,0)), ...)
prior$B$V[2,2]<-1e-8

or something similar, achieves this.


>
> Based on some online readings etc. I came up with a model and a  
> prior, but I am not feeling very confident about it, could you  
> please indicate if this model makes sense?
>
> prior0 <- list(B=list(mu = matrix(0,10,2),
> V  = diag(10)*1e+6),
>                             R  = list(V=diag(2),n=2,fix=2),
>                             G  = list(G1=list(V=diag(c(1,  
> 1e-6)),n=2, fix=2)))
>
> m.zip <-  MCMCglmm(AE ~ trait + trait:(LONGITUDE*LATITUDE) + trait:sst,
>                             random = ~idh(trait):YEAR,
> family = "zipoisson",
> rcov = ~ idh(trait):units,
>                             prior = prior0,
> nitt = 100000,
> burnin = 10000,
> thin = 25,
> data = eggs)
>
> m.zap <-MCMCglmm(AE ~ trait + trait:(LONGITUDE*LATITUDE) + trait:sst,
>                             random = ~idh(trait):YEAR,
> family = "zapoisson",
> rcov = ~ idh(trait):units,
>                             prior = prior0,
> nitt = 100000,
> burnin = 10000,
> thin = 25, data = eggs)
>
>

If you only want to fit random effects for the count process

random = ~idh(at.level(trait,1)):YEAR

is probably a better way of doing it. This just fits a single variance  
rather than a 2x2 covariance matrix.

Your prior degrees of freedom are large. With idh structures you have  
nu=2 on a single variance. I would use something smaller (e.g. 0.002)  
or preferably parameter expanded priors.

> Plotting and looking at the summary both models works fine, but I  
> cannot figure out how to predict the data. I tried the following,  
> but get an Error message (which I do not understand):
> predict(m.zip, marginal = ~idh(trait):YEAR, type = "response",  
> interval = "confidence")
> Error in M[, which(rm.v), ] <- 0 : incorrect number of subscripts

the predict method does not work with ZIP models yet, so you will have  
to do it by hand I'm afraid. The expected value is (1-pi)*lambda where  
pi is the probability of being zero from the zero-inflation part of  
the model, and lambda is the Poisson rate (in the CourseNotes  
notation: (1-plogis(l_2))*exp(l_2)).

I am not sure what the expectation would be after marginalising the  
random effects/overdispersion, particularly if the two processes are  
correlated (which they are not in your model).

Cheers,

Jarrod






>
> Any help is greatly appreciated and many thanks in advance,
>
> Sven Gastauer
>
> IMARES
> Fisheries Acoustician
> Email: sven.gastauer at wur.nl<mailto:sven.gastauer at wur.nl>
> Mobile: +31 (0)61 005 71 03
>
> P.O. Box 68
> Haringkade, 1 (0.23)
> 1970AB IJMUIDEN
>
>
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