[R-sig-ME] Fwd: priors for multivariate mixed model in MCMCglmm with random intercepts and slopes

[John Morrongiello]

Hi Malcolm thanks for the suggestions regarding the priors. Changing the 7
to an 8 for the random effect priors worked a treat, as did your
specification for uninformative priors. The model runs and results are
sensible.

In regards to your other questions about the data and model specification:
I lied a bit in outlining the level of coverage. Some individuals have the
7 observations across each of 124 time periods, others less. This is partly
because of different aged individuals and also because I ensured that I'm
only analysing data from a given time point for an individual when all 7
response variables are present. I allow Age to randomly vary across months
because the month term captures most of the extrinsic sources of variation
in the model without specifying what this is (obviously this can be
attributed when environmental terms are added to the model). It is highly
likely thathow an individual responds to a change in the environment is age
dependent, hence the random age slope on month (which just so happens to
greatly improve model performance).

Finally, I model growth as opposed to size at age as we only have
information from the otolith on increment width which is a proxy for
growth. I could do some form of back-calculation to convert increment
measurements into fish size, but this process is not perfect and can
introduce bias into the data. Also, I find model interpretation easier when
I talk about growth (e.g. conditions in year x were good for growth, warm
temperatures favour higher growth) rather than changes in fish size, which
is very much conditional on the size of fish at the previous time step, and
the range of fish that contribute to a given section of the chronology.

Cheers
John



On Sat, Jan 24, 2015 at 5:49 AM, Malcolm Fairbrother <
M.Fairbrother at bristol.ac.uk> wrote:

> Hi John,
>
> This is not my substantive area of expertise at all, and I'm not
> completely confident I can help. But, nobody else has responded, and I have
> fitted some multivariate models with MCMCglmm. So, for what it's worth...
>
> For starters, I'm not sure I understand the data. If you're saying each of
> 7 properties are observed on 38 fish each observed over the course of 124
> months, where does 1021 come from? (38x124 is 4712...) Are you saying you
> have repeated observations on fish over the course of 124 months, but for
> each actual fish you have fewer observations than 124?
>
> Next, two questions about your models:
> Why do you allow the slope for Age to vary randomly across months?
> And why model growth (so, say, % or absolute change in length) rather than
> the property that is growing (length)? The latter would seem more
> straightforward to me.
>
> As regards the priors, if I understand you correctly, you've kept the same
> prior specification (prior1) when fitting models (m3 and m4) with an
> additional parameter at each higher level. So maybe try changing 7 to 8 at
> those levels?
>
> prior2  <- list(R=list(V=diag(7), nu=7), G=list(G1=list(V=diag(8), nu=8),
> G2=list(V=diag(8), nu=8)))
>
> Additionally, also for what it's worth, I've found parameter-expanded
> priors to be more uninformative, and Jarrod has made them pretty easy to
> use. So (assuming you want them to be uninformative) you might try:
>
> prior2a  <- list(R=list(V=diag(7), nu=7.02), G=list(G1=list(V=diag(8),
> nu=8.02, alpha.mu=rep(0,8), alpha.V=1000*diag(8)), G2=list(V=diag(8),
> nu=8.02, alpha.mu=rep(0,8), alpha.V=1000*diag(8))))
>
> Hope that helps...?
>
> Don't feel bad. You're far from the first person to write to this list
> with questions about priors for MCMCglmm!
>
> Cheers,
> Malcolm
>
>
>
>
>> Date: Thu, 22 Jan 2015 22:23:26 +1100
>> From: John Morrongiello <jrmorrongiello at gmail.com>
>> To: r-sig-mixed-models at r-project.org
>> Subject: [R-sig-ME] Fwd: priors for multivariate mixed model in
>>         MCMCglmm with random intercepts and slopes
>>
>> Just wondering if anyone has any thoughts on this question about MCMCglmm
>> priors for a multivariate mixed model with random intercepts and slopes?
>>
>> ---------- Forwarded message ----------
>> From: John Morrongiello <jrmorrongiello at gmail.com>
>> Date: Sun, Jan 18, 2015 at 3:56 PM
>> Subject: priors for multivariate mixed model in MCMCglmm with random
>> intercepts and slopes
>> To: r-sig-mixed-models at r-project.org
>>
>> Hi
>> I've got a data set with 7 response variables measured monthly through
>> time
>> across 38 individuals (FishID). There are 124 months (MonthCode)
>> representing each sampling time, with the data set having 1021
>> observations
>> in total. I have previously analysed this data using a series of
>> univariate
>> mixed models fitted in lme4 of the form
>>
>> m1<-lmer(AvGrowth~ Age + (Age|FishID) + (Age|MonthCode), data=alldata1)
>> .....mx<-lmer(.....)
>>
>> Here, Age is a continuous covariate that models an age-dependent decline
>> in
>> growth; the slope of this relationship allowed to vary amongst individuals
>> (FishID) and through time (MonthCode). To this model structure I have also
>> added environmental effects like temperature etc.
>>
>> As the 7 response variables are all measured at the same time from each
>> fish (they are estimates of growth and otolith microchemistry), I thought
>> to fit a multivariate mixed model to estimate covariances and also
>> succinctly ascertain the importance of various environmental effects.
>>
>> I have had success fitting m2 below where the overall model intercept is
>> suppressed and the trait-dependent iAge effect is allowed to vary by
>> individual and MonthCode (similar to m1):
>>
>>
>> prior1<-list(R=list(V=diag(7),nu=7),G=list(G1=list(V=diag(7),nu=7),G2=list(V=diag(7),nu=7)))
>>
>>
>> m2<-MCMCglmm(cbind(AvGrowth.std,NaCa.std,SrCa.std,logMgCa.std,logBca.std,logBaCa.std,logLiCa.std)
>> ~(trait + trait:Age -1),
>> random=~us(trait:Age):FishID + us(trait:Age):MonthCode,
>> rcov=~us(trait):units,
>> family=rep("gaussian",7), prior=prior1,
>> nitt=60000,thin=25,burnin=10000, data=alldata1,verbose=FALSE)
>>
>> When I use posterior.mode(m2$VCV) however, I don't get estimates of the
>> random intercept terms FishID and MonthCode, nor their covariance with
>> Age,
>> rather just variances dependent on the iAge slope (e.g.
>> AvGrowth.std:Age):AvGrowth.std:Age).FishID). I therefore tried to
>> explicitly code a correlated random intercept and slope using us(1+
>> trait:(Age):FishID in m3:
>>
>>
>> m3<-MCMCglmm(cbind(AvGrowth.std,NaCa.std,SrCa.std,logMgCa.std,logBca.std,logBaCa.std,logLiCa.std)
>> ~(trait + trait:Age -1),
>> random=~us(1+ trait:Age):FishID + us(1+ trait:Age):MonthCode,
>> rcov=~us(trait):units,
>> family=rep("gaussian",7), prior=prior1,
>> nitt=60000,thin=25,burnin=10000, data=alldata1,verbose=FALSE)
>>
>> This returns the error:
>> Error in priorformat(if (NOpriorG) { :  V is the wrong dimension for some
>> prior$G/prior$R elements
>>
>> So I'm tipping something is wrong with my priors. m4, where I estimate an
>> overall model intercept and specific random intercepts also returns the
>> same error.
>>
>>
>> m4<-MCMCglmm(cbind(AvGrowth.std,NaCa.std,SrCa.std,logMgCa.std,logBca.std,logBaCa.std,logLiCa.std)
>> ~(trait + trait:Age +1),
>> random=~us(1+ trait:Age):FishID + us(1+ trait:Age):MonthCode,
>> rcov=~us(trait):units,
>> family=rep("gaussian",7), prior=prior1,
>> nitt=60000,thin=25,burnin=10000, data=alldata1,verbose=FALSE)
>>
>> Would someone have some tips about how to get the priors for m3 and m4
>> working? I've worked through the course notes and read some email posts,
>> but admit that I a little at sea in terms of understanding the specifics
>> of
>> what is being coded on the prior side of things.
>>
>> Cheers
>>
>> John
>>
>
>

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