HPD intervals for fixed parameters in model

Mon, Jun 4, 2012 6:36 PM

Log transforming the Age variable prior to putting it in the model solved the problem of a random slope in glmmADMB. 

Thanks also to Ben for the note about the different covariance matrices in use. I did a bit more reading on this, especially for MCMCglmm, and came up with the following model structures. Are the following lmer, MCMCglmm and glmmADMB roughly comparable?

*Variation in fish intercepts, variation in Age slopes, correlation between intercept and slope:

M1lmer<-lmer(log(Increment)~logAge+temp+(logAge|FishID)+(1|fYear),data,REML=T)
M1mcmc<-MCMCglmm(log(Increment)~logAge+temp,random=~us(1+logAge):FishID + fYear,rcov= ~units, data=data, prior=prior)##us allows for intercept and slope covariance
##not possible with glmmADMB??

* Variation in fish intercepts and age slopes, but no correlation between intercept and slope:

M2lmer<-lmer(log(Increment)~logAge+temp+(1+FishID)+(0+logAge|FishID)+(1|Year),data,REML=F)##REML= FALSE is equivalent to glmmADMB?
M2mcmc<-MCMCglmm(log(Increment)~logAge+temp,random=~idh(1+logAge):FishID + fYear,rcov= ~units, data=data, prior=prior)##idh sets covariance between intercept and slope to zero (also could use idh(logAge):FishID+FishID)
M2glmmADMB<-glmmadmb(log(Increment)~logAge+temp+(logAge|FishID)+(1|fYear),NSWtiger,family='gaussian')

Cheers

John

-----Original Message-----
From: Ben Bolker [mailto:bbolker at gmail.com] 
Sent: Monday, 4 June 2012 5:12 PM
To: Morrongiello, John (CMAR, Hobart)
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] HPD intervals for fixed parameters in model

On 12-06-04 03:03 AM, John.Morrongiello at csiro.au wrote:

As a quick possible workaround, try defining data$logAge <-
log(data$Age) and using (logAge|FishID) in your model formula; I'm not
sure that glmmADMB can handle defining variable transformations on the
fly in that context.

  Also be aware that the default for lme4 is to use the full correlation
matrix while glmmADMB uses a diagonal matrix, so (e.g.) (logAge|FishID)
would estimate three parameters (variation in intercept across fish,
variation in slope across fish, covariance between intercept and slope)
while glmmADMB would only estimate the first two.  (I think you have to
specify this choice explicitly in MCMCglmm.)


Message: 4
Date: Fri, 1 Jun 2012 16:44:51 +0000 (UTC)
From: Ben Bolker <bbolker at gmail.com>
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] HPD intervals for fixed parameters in model
	with	crossed and correlated random effects
Message-ID: <loom.20120601T183904-68 at post.gmane.org>
Content-Type: text/plain; charset=us-ascii

 <John.Morrongiello at ...> writes:

I'd very much like to calculate some HPD intervals for the fixed
parameters in a lmer model containing crossed and correlated random
effects. However, I have not been able to find a solution for this
type of model after a pretty thorough search of discussion threats
or worked examples. Is this possible at the moment with lme4
(function or work around), or do I have to change packages and try
something like mcmcglmm?

  I think if you want to compute HPD intervals you are more or less
stuck with MCMCglmm or glmmADMB ....

My data contains 1917 growth measurements (Increment) from 704 fish
(FishID) and the data is sampled from 29 years (Year). I'm
interested in the effects of age (2-18 years) and water temperature
(temp) on growth.  My model is:

M1<-lmer(log(Increment)~log(Age)+temp+(log(Age)|FishID)+(1|Year),
  data,REML=T)

HPDinterval requires an mcmc object, but when I try
mcmcsamp(M1, n=1000)

I receive the following error:
Error in .local(object, n, verbose, ...) :
  Code for non-trivial theta_T not yet written

I understand this is because MCMCsamp doesn't yet cope with
correlated random effects? On the glmm wikidot page there is code to
generate confidence and prediction intervals on predictions- could I
use some of N this to get a what I'm after (if so, which bits)? I
haven't used mcmcglmm before, so ideally would like to stay with the
more familiar lme4 if possible to expedite the analyses!

   I don't think so, I think you'll need MCMCglmm or glmmADMB.

In principle glmmADMB should work with your model more or less as-is
(although I don't remember whether it can do REML-y stuff or not),
and you can use mcmc=TRUE to get it to run an MCMC chain on the
parameters for you.  However, based on my limited experience, if
you do want to get MCMC working it will be easier using MCMCglmm
(which is intrinsically based on MCMC, and does a bunch of clever
stuff to make the chains mix well).

  good luck,
    Ben Bolker

HPD intervals for fixed parameters in model

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