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

[Samantha Patrick]

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)
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/