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

Jarrod Hadfield j.hadfield at ed.ac.uk
Mon Jan 4 09:16:05 CET 2016 

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
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>
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>>>>> Scotland, with registration number SC005336.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>
>>> --
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>>>
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>>> R-sig-mixed-models at r-project.org mailing list
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>>
>>
>


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