[R-sig-ME] MCMCglmm error-in-variables (total least squares) model?

Alberto Gallano alberto.gc8 at gmail.com
Tue Jan 5 05:49:51 CET 2016


Hi Jarrod,

that's great - I think I understand what that model is doing. If you could
forward the information about the tutorial and paper (if it's published
yet) that would be very helpful. Thanks a lot.

best,
Alberto

On Mon, Jan 4, 2016 at 3:16 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk> wrote:

> Hi,
>
> The least parsimonious model (and not the one I would necessarily
> recommend fitting) is:
>
>
> m1<-MCMCglmm(cbind(X1,X2,X3,Y)~trait,
>              random=~us(trait):species+us(trait):species.ide,
>              rcov=~us(trait):units,
>              ginverse=list(species=tree))
>
> where species and species.ide are columns of species names.
>
> This deals with the measurement error on the species means, and also
> allows you to address the fact that the regressions of the X's on Y may be
> different at different levels. The method advocated by van de Pol has the
> problem that the mean in the mean centering is just the observed mean
> rather than the true unobserved mean. For example, imagine that you only
> had one observation for some of the species.  You can obtain the regression
> coefficients at each level, by using the relationship beta =
> VAR(X)^{-1}COV(X,Y). For example, the posterior distribution of the
> regression coefficients at the phylogenetic level would be:
>
>
> reg.coef<-function(x, X=1:3, Y=4){
> V<-matrix(x,c(X,Y),c(X,Y))
> solve(V[X,X], V[X,Y])
> }
>
> apply(m1$VCV[,1:16], 1, reg.coef)
>
> The model doesn't deal with measurement error on the individual
> measurements, but if you had repeat measurements per individual you could
> also fit these (as a diagonal matrix, rather than unstructured).
>
> After taking into account measurement error, some people suggest that
> species.ide should be dropped from the model. I am not completely convinced
> by this argument.
>
> Priors are going to be a pain in this model.
>
> You could replace the us structures by ante3 structures. The model is then
> fitted directly in terms of the regression coefficients. Antedependence
> regression coefficients 3,5,6 are the regressions of X3, X2 and X1 on Y. If
> you are interested in this we have a mini-tutorial associated with a
> recently submitted paper I can send you.
>
> Cheers,
>
> Jarrod
>
>
>
>
>
>
>
> Quoting Alberto Gallano <alberto.gc8 at gmail.com> on Sun, 3 Jan 2016
> 15:45:26 -0500:
>
> Hi Jarrod,
>>
>> yes, that's right, I have multiple measurements for both response and
>> predictors and these are measured on the same individuals. The model i'm
>> fitting is very similar to the model called "model_repeat2" from Modern
>> Phylogenetic Comparative Methods:
>>
>>
>> http://www.mpcm-evolution.org/practice/online-practical-material-chapter-11/chapter-11-2-multiple-measurements-model-mcmcglmm
>>
>> same random effects structure, same between/within structure for the fixed
>> effects, and i'm also using the inverse of the matrix of phylogenetic
>> correlation.
>>
>> @Dimitri: I'm aware of the de Villemereuil et al. approach, which, If I
>> understand correctly, does a version of orthogonal regression (in JAGS).
>> I'm trying find out if this is possible in MCMCglmm.
>>
>> best,
>> Alberto
>>
>> On Sun, Jan 3, 2016 at 12:05 PM, Dimitri Skandalis <
>> da.skandalis at gmail.com>
>> wrote:
>>
>> Hi Alberto,
>>>
>>> Have you looked at the book Modern Phylogenetic Comparative Methods? R
>>> code provided with Chapter 11 (2) deals with correlated measurements, and
>>> could be a good place to start.
>>>
>>>
>>> http://www.mpcm-evolution.org/practice/online-practical-material-chapter-11
>>>
>>> Also, de Villemereuil et al. have developed an approach to related models
>>> in BUGS/JAGS.
>>>
>>> http://bmcevolbiol.biomedcentral.com/articles/10.1186/1471-2148-12-102
>>>
>>> Dimitri
>>>
>>> On Sun, Jan 3, 2016 at 8:16 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk>
>>> wrote:
>>>
>>> Hi Alberto,
>>>>
>>>> When you say you have multiple observations for each species, do you
>>>> mean
>>>> that you have multiple observations for the response and the
>>>> predictors? Do
>>>> you expect the response and/or the predictors to be correlated at the
>>>> observation level (for example are they measured on the same
>>>> individuals)?
>>>> I presume the answer to both these questions is yes if you wish to use
>>>> the
>>>> van de Pol method?
>>>>
>>>> Cheers,
>>>>
>>>> Jarrod
>>>>
>>>>
>>>> Quoting Alberto Gallano <alberto.gc8 at gmail.com> on Sun, 3 Jan 2016
>>>> 10:35:02 -0500:
>>>>
>>>> Hi Jarrod,
>>>>
>>>>>
>>>>> I don't know the measurement error in the predictors in advance, so I
>>>>> guess
>>>>> it would need to be estimated simultaneously. I'm not 100% sure what
>>>>> you
>>>>> mean by 'multiple observations for each predictor variable'. I have
>>>>> data
>>>>> on
>>>>> 132 species and have multiple observations (7 to 80) for each species.
>>>>> I'm
>>>>> using a species level random effect and a phylogenetic covariance
>>>>> matrix
>>>>> (using ginverse) to account for phylogenetic autocorrelation, and I'm
>>>>> also
>>>>> using van de Pol and Wright's (2009) method for partitioning slopes
>>>>> into
>>>>> between- and within-species (i'm interested in the between species
>>>>> slope).
>>>>> My understanding is that neither of these things fits a model in which
>>>>> orthogonal residuals are minimized.
>>>>>
>>>>> best,
>>>>> Alberto
>>>>>
>>>>>
>>>>> On Sun, Jan 3, 2016 at 5:24 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk>
>>>>> wrote:
>>>>>
>>>>> Hi Alberto,
>>>>>
>>>>>>
>>>>>> Do you know the measurement error in the predictors in advance or do
>>>>>> you
>>>>>> have multiple observations for each predictor variable and wish to
>>>>>> estimate
>>>>>> the error simultaneously?
>>>>>>
>>>>>> Cheers,
>>>>>>
>>>>>> Jarrod
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> Quoting Malcolm Fairbrother <M.Fairbrother at bristol.ac.uk> on Sat, 2
>>>>>> Jan
>>>>>> 2016 14:47:08 -0800:
>>>>>>
>>>>>> Dear Alberto (I believe),
>>>>>>
>>>>>> To my knowledge, this is not possible in MCMCglmm (though Jarrod
>>>>>>> Hadfield,
>>>>>>> the package author, may weigh in with another response).
>>>>>>> A collaborator and I have been working on a paper that shows how to
>>>>>>> fit
>>>>>>> such models in JAGS (and perhaps Stan), though thus far we've only
>>>>>>> been
>>>>>>> able to fit such models correcting for measurement error in the
>>>>>>> predictors
>>>>>>> at the lowest level. Multiple such predictors (including with
>>>>>>> different
>>>>>>> measurement error variances) are no problem.
>>>>>>> That paper, however, is probably still some months away from being
>>>>>>> finished
>>>>>>> and presentable. In the meantime, I don't know of any good options
>>>>>>> for
>>>>>>> you.
>>>>>>> If other subscribers to this list have any ideas, I'll be quite
>>>>>>> interested
>>>>>>> too!
>>>>>>> - Malcolm
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Date: Tue, 29 Dec 2015 16:09:53 -0500
>>>>>>>
>>>>>>> From: Alberto Gallano <alberto.gc8 at gmail.com>
>>>>>>>
>>>>>>>> To: r-sig-mixed-models at r-project.org
>>>>>>>> Subject: [R-sig-ME] MCMCglmm error-in-variables (total least
>>>>>>>> squares)
>>>>>>>>         model?
>>>>>>>>
>>>>>>>> I posted this question on Stack Overflow a week ago but received no
>>>>>>>> answers:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> http://stackoverflow.com/questions/34446618/bayesian-error-in-variables-total-least-squares-model-in-r-using-mcmcglmm
>>>>>>>>
>>>>>>>> This may be a more appropriate venue.
>>>>>>>>
>>>>>>>>
>>>>>>>> I am fitting some Bayesian linear mixed models using the MCMCglmm
>>>>>>>> package.
>>>>>>>> My data includes predictors that are measured with error. I'd
>>>>>>>> therefore
>>>>>>>> like to build a model that takes this into account. My understanding
>>>>>>>> is
>>>>>>>> that a basic mixed effects model in MCMCglmm will minimize error
>>>>>>>> only
>>>>>>>> for
>>>>>>>> the response variable (as in frequentist OLS regression). In other
>>>>>>>> words,
>>>>>>>> vertical errors will be minimized. Instead, I'd like to minimize
>>>>>>>> errors
>>>>>>>> orthogonal to the regression line/plane/hyperplane.
>>>>>>>>
>>>>>>>>    1. Is it possible to fit an error-in-variables (aka total least
>>>>>>>> squares)
>>>>>>>>    model using MCMCglmm or would I have to use JAGS / STAN to do
>>>>>>>> this?
>>>>>>>>    2. Is it possible to do this with multiple predictors in the same
>>>>>>>> model
>>>>>>>>    (I have some models with 3 or 4 predictors, each measured with
>>>>>>>> error)?
>>>>>>>>
>>>>>>>>
>>>>>>>>         [[alternative HTML version deleted]]
>>>>>>>>
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> R-sig-mixed-models at r-project.org mailing list
>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> --
>>>>>> The University of Edinburgh is a charitable body, registered in
>>>>>> Scotland, with registration number SC005336.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>> --
>>>> The University of Edinburgh is a charitable body, registered in
>>>> Scotland, with registration number SC005336.
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>
>>>>
>>>
>>>
>>
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
>
>

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