[R-sig-ME] Bivariate MCMCglmm with repeated measures
Jarrod Hadfield
j.hadfield at ed.ac.uk
Wed Aug 13 16:09:11 CEST 2014
Hi,
To do piecewise random regression forcing the two regression to `join'
you could centre your covariate (Time) at the breakpoint. Then use:
random = ~us(1 + at.level(stage,1):Time+at.level(stage,2):Time):Individual
The first variance is the variance in the new intercepts (the value at
the breakpoint) and the other two variances are the variances in
slopes that emanate from either side of the breakpoint.
Bear in mind you will need a lot of data to get precise estimates from
such a complex model, particularly if you want to break it up by sex
too.
Cheers,
Jarrod
Quoting "PATRICK, Samantha" <spatrick at glos.ac.uk> on Wed, 13 Aug 2014
13:53:58 +0000:
> Hi Jarrod
>
> Thanks for getting back to me. By simplifying the data, I left out
> the fact that there is a temporal pattern (Time). There is an
> interaction between Time * Stage on Presence. During stage one,
> Presence increases linearly with Time; during stage two Presence
> decreases linearly with time. Stage one and two are mutually
> exclusive: Time 1-5 is always stage 1 and Time 6-10 always stage 2.
> This was why I was originally to fit a bivariate model, so I could
> calculate the covariance between the slopes.
>
> Following the method you suggested I have been able to progress
> towards this. The following model, if I understand correctly, fits
> an intercept (stage; two level factor) and a two population slopes
> (One in stage 1 and one in stage 2) and then a random intercept and
> slope during stage one and another random intercept and slope during
> stage two. The 4x4 covariance matrix estimates the covariance
> between both intercepts and both slopes.
> ### this prior is not optimised in anyway - it is just a starting point
> prior2.1 <- list(G = list(G1 = list(V=diag(4), nu=2,
> alpha.mu=c(0,0,0,0), alpha.V=diag(4)*1000)),
> R = list(V=1, fix=1))
>
> ## full model
> model2.1 <- MCMCglmm(Presence~ stage + at.level(stage,1):Time +
> at.level(stage,2):Time ,
>
> random = ~us(at.level(stage ,1)+ at.level(stage ,1):Time +
> at.level(stage ,2) +at.level(stage
> ,2):Time):Individual,
>
> rcov = ~units, family = "categorical",
>
> data = Data2, prior = prior2.1, verbose = FALSE, pr=T)
>
> I then extended this model to allow the covariance structure to vary
> between the sexes:
>
> ##prior
> prior2.2<- list(G = list(G1 = list(V=diag(8), nu=2,
> alpha.mu=c(0,0,0,0,0,0,0,0), alpha.V=diag(8)*1000)),
> R = list(V=1, fix=1))
>
> ## full model
> model2.2<- MCMCglmm(Presence~ stage + at.level(stage,1):Time +
> at.level(stage,2):Time ,
> random = ~us(at.level(stage,1):at.level(Sex,1)+
> at.level(stage,1):at.level(Sex,2)+
> at.level(stage,1):at.level(Sex,1):Time +
> at.level(stage,1):at.level(Sex,2):Time +
> at.level(stage,2):at.level(Sex,1)+
> at.level(stage,2):at.level(Sex,2)+
> at.level(stage,2):at.level(Sex,1):Time +
>
> at.level(stage,2):at.level(Sex,2):Time ):Individual,
> rcov = ~units, family = "categorical",
> data = Data2, prior = prior2.2, verbose = FALSE, pr=T)
>
> So I am left with one question: In essence the data lends itself to
> a piecewise regression, such that the end point of the slope in
> stage one is the start point for stage two. Is it possible to fit
> this at the individual level? By this I mean that the random slope
> for individual 1 at stage two begins where and the slope for stage
> one ends. I have struggled to find anyone doing this.
>
> I have included the full models and simulated data below (runs in
> first model only) in case anyone else is working on this kind of
> problem.
>
> Thanks
>
> Sam
>
>
> ### Data
>
>
> Time
> Presence Stage Individual
> 1 1 1 1
> 2 1 1 1
> 3 0 1 1
> 4 1 1 1
> 5 1 1 1
> 6 0 2 1
> 7 0 2 1
> 8 1 2 1
> 9 0 2 1
> 10 1 2 1
> 1 0 1 2
> 2 1 1 2
> 3 0 1 2
> 4 1 1 2
> 5 1 1 2
> 6 1 2 2
> 7 0 2 2
> 8 0 2 2
> 9 0 2 2
> 10 1 2 2
> 1 0 1 3
> 2 1 1 3
> 3 1 1 3
> 4 1 1 3
> 5 1 1 3
> 6 0 2 3
> 7 0 2 3
> 8 1 2 3
> 9 1 2 3
> 10 1 2 3
> 1 0 1 4
> 2 1 1 4
> 3 1 1 4
> 4 1 1 4
> 5 1 1 4
> 6 1 2 4
> 7 1 2 4
> 8 0 2 4
> 9 0 2 4
> 10 0 2 4
> 1 1 1 5
> 2 0 1 5
> 3 0 1 5
> 4 1 1 5
> 5 1 1 5
> 6 1 2 5
> 7 1 2 5
> 8 1 2 5
> 9 1 2 5
> 10 0 2 5
>
>
> Dr Samantha Patrick
> Research Fellow
> Biosciences QU116
> Francis Close Hall Campus
> University of Gloucestershire
> Cheltenham, GL50 4AZ, UK
>
> Research Associate: OxNav, University of Oxford
>
> ******From 1st August - 14th November 2014 I will be
> based in Montréal, which is 5 hours behind GMT ******
>
> Tel: 07740 472 719
> Skype: sammy_patrick
> https://sites.google.com/site/samanthacpatrick/
>
> From: Jarrod Hadfield<mailto:j.hadfield at ed.ac.uk>
> Sent: Monday, 11 August 2014 14:47
> To: Samantha Patrick<mailto:spatrick at glos.ac.uk>
> Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
>
> Hi Sam,
>
> One option would be
>
> random = ~us(stage):Individual, rcov=~units
>
> where the random term is a 2x2 covariance matrix (between individual
> variances for each stage and the covariance between them). There is
> only a single residual variance in my model - but this is OK, with
> binary data it can't be estimated so there is no point trying to
> estimates separate residual variances for each stage. You will need to
> fix the residual variance at something though (I use 1).
>
> If you only have Individual level covariates (i.e. no
> observation-level covariates) then you could group your binary
> responses into a binomial response and fit the model
>
> random=NULL, rcov = ~us(stage):units
>
> This will give (nearly) the same answers as the first model if you
> rescale the (co)variances as described in the CourseNotes. It will be
> much faster too.
>
> You might also want to consider models that deal with temporal
> autocorrelation, but these are not implemented in MCMCglmm.
>
> Cheers,
>
> Jarrod
> Quoting "PATRICK, Samantha" <spatrick at glos.ac.uk> on Mon, 11 Aug 2014
> 17:34:05 +0000:
>
>> Hi
>>
>> I running a bivariate GLMM, where both of my response variables have
>> repeated measures. A dummy data set would look like this:
>>
>> Individual Presence Stage
>> 1 0 1
>> 1 1 1
>> 1 1 2
>> 1 1 2
>> 2 1 1
>> 2 0 1
>> 2 0 1
>> 2 1 2
>> 2 0 2
>>
>> There are a series of individuals. For each individual we have
>> measures presence/absence repeatedly during life stage 1 and then
>> again repeatedly during life stage 2.
>>
>> For a straight forward bivariate model, with a single measure per
>> individual (or repeated measures during only one life stage), the
>> data could be set up like this:
>>
>> Individual Presence stage 1 Presence stage 2
>>
>> However because I have repeated measures for both stages I am
>> struggling to find out how to code the data so MCMCglmm can run.
>>
>> Does anyone have any experience with this kind of data structure? I
>> can’t find anything on the R list.
>>
>> Many Thanks
>>
>> Sam
>>
>> Dr Samantha Patrick
>> Research Fellow
>> Biosciences QU116
>> Francis Close Hall Campus
>> University of Gloucestershire
>> Cheltenham, GL50 4AZ, UK
>>
>> Research Associate: OxNav, University of Oxford
>>
>> ******From 1st August - 14th November 2014 I will be
>> based in Montréal, which is 5 hours behind GMT ******
>>
>> Tel: 07740 472 719
>> Skype: sammy_patrick
>> https://sites.google.com/site/samanthacpatrick/
>>
>> -
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>
>
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