[R-sig-ME] Calculating repeatability with ordinal data

[Jarrod Hadfield]

Hi,

The residual variance can never be estimated from ordinal data. Most  
programs will set it to zero, some programs allow you to set it at  
anything (MCMCglmm). I have not seen repeatabilities for ordinal data  
but I presume you can add the variance of the relevant distribution  
(pi^2/3 or 1 for logit/probit) to the denominator in order to get an  
intra-class correlation. I'm not confident how this would be  
interpreted for an ordinal response though. Note that if you do use  
MCMCglmm you need to include the constrained residual variance in the  
denominator (i.e. to get the denominator you need to add two to the  
"Bird" variance if you have constrained the residual variance to one).

Cheers,

Jarrod


Quoting Samantha Patrick <spatrick at cebc.cnrs.fr> on Wed, 02 May 2012  
13:11:09 +0200:

> Hi
>
> Thank you for the tip - I had editted my code!  However, sadly it  
> doesn't  solve the problem of how to estimate the residual variance.
>
> Many Thanks
>
> Sam
>
>
> Le 02/05/2012 12:38, Federico Calboli a écrit :
>> On 2 May 2012, at 11:08, Samantha Patrick wrote:
>>
>>> Hi
>>>
>>> Firstly I sent this message last week but can find no evidence  
>>> that it actually sent.
>>> However, if this is a double posting I am very sorry.
>>>
>>> I am currently working with repeated measures for individuals and I am
>>> trying to quantify individual repeatability.  Normally, for continuous
>>> distributions, I would use a mixed model and calculate the variance
>>> explained by individual divided by the total variance.  However my  
>>> individual scores
>>> are ordinal and I have been using the clmm function in the Ordinal package:
>>>
>>> example of data:
>>> ID        Bird        Sex    scoremax    year
>>> 622    BS8831    M       2                 2008
>>> 623    BS8831    M       1                 2010
>>> 624    BS8831    M       1                 2011
>>> 625    BS9065    M       1                 2010
>>> 626    BS9065    M       3                 2011
>>> 627   BS19724    F       4                 2010
>>> 628   BS19724    F       5                 2010
>>> 629   BS21302    F       1                 2010
>>> 630   BS25376    F       1                 2011
>>> 631    BS9184    F       2                 2009
>>> 632   BS19989    M       3                 2011
>>> 633   BS21617    M       4                 2008
>>> 634   BS21617    M       2                 2009
>>> 635   BS21617    M       1                 2010
>>>
>>> where scoremax ranges from 1-5, and there are 1188 birds and 1638
>>> observations.
>>>
>>> scoremax<-as.factor(scoremax)
>> does
>>
>> scoremax = as.ordered(scoremax)
>>
>> make any difference in your results?
>>
>> I ask this because as.factor() does not, strictly speaking, create  
>> an ordered factor.
>>
>> BW
>>
>> F
>>
>>
>>
>>
>>> bird<-as.factor(bird)
>>> year<-as.factor(year)
>>> fmm1<- clmm(scoremax~year+ (1|bird), link = c("probit"), Hess =TRUE)
>>>
>>> summary(fmm1)
>>>
>>> but this only gives the variance estimate for bird, with no residual
>>> estimate.  Some investigations reveal that using an ordinal regression
>>> in MCMCglmm will also not estimate the residual variance, and it seems
>>> you need to constrain this value.  I have been unable to find any posts
>>> about repeatability in ordinal data.
>>>
>>> My questions I guess are:
>>> Is using a mixed model appropriate for calculating the repeatability of
>>> ordinal data (and if not does anyone know any other methods)?
>>>
>>> If it is, does anyone have any hints on how to calculate the  
>>> residual variance,
>>> to enable repeatability estimates to be calculated.
>>>
>>> Many Thanks
>>>
>>> Sam
>>>
>>> -- 
>>>
>>> Dr Samantha Patrick
>>> Post Doctoral Fellow
>>> Centre d'Etudes Biologiques de Chizé - CNRS
>>> 79360 Villiers-en-Bois
>>> France
>>> T:+33 549 097 846
>>> M:+33 675 603 451
>>> Skype: sammy_patrick
>>> http://www.cebc.cnrs.fr/Fidentite/patrick/patrick.htm
>>> http://www.researchgate.net/profile/Samantha_Patrick/
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>> --
>> Federico C. F. Calboli
>> Neuroepidemiology and Ageing Research
>> Imperial College, St. Mary's Campus
>> Norfolk Place, London W2 1PG
>>
>> Tel +44 (0)20 75941602   Fax +44 (0)20 75943193
>>
>> f.calboli [.a.t] imperial.ac.uk
>> f.calboli [.a.t] gmail.com
>>
>>
>>
>
> -- 
>
> Dr Samantha Patrick
> Post Doctoral Fellow
> Centre d'Etudes Biologiques de Chizé - CNRS
> 79360 Villiers-en-Bois
> France
> T:+33 549 097 846
> M:+33 675 603 451
> Skype: sammy_patrick
> http://www.cebc.cnrs.fr/Fidentite/patrick/patrick.htm
> http://www.researchgate.net/profile/Samantha_Patrick/
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>



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