> Dear Arthur,
>
> I don't know if you've read the paper I wrote its title and source in the
> cover of your workshop in the Uni Melb. I need your help to answer a
> question related to this paper:
>
> Is this valid to directly estimate (co)variance components hence
> heritability and genetic correlation for categorial traits without
> transforming them? What's the consequence if this is not?
>
Dear Xianming,
At last I have scanned the paper and got back to your question.
My answer is YES it is valid but it may not be fully optimal or efficient.
A few quick comments follow. I will send this to the list incase others
wish to comment.
Categorical traits are of various sorts. Usually they are
regarded as an approximation to an underlying variable of interest.
The basic assumption is that there is a monotonic relationship.
Presumably the categorical trait arises becasue it is not possible to
measure the real variable of interest.
So, provided the relationship is monotonic, it will be approximately linear
(to an unknown degree depending on the trait) and so normal analysis of
the score will usually give a good idea of what is happening.
The usual problem is that there may be a mean/variance relationship.
This applies when the distribution is most skewed. In other words,
the more 'normal' the distribution of scores, the happier you will
be with a normal analysis.
Problems occur with binomial data if the mean incidence is quite variable
across groups including some with extreme (outside .10 .90 interval) values.
ASREML can fit an animal model using GLMM (Schall type) assumptions
to binomial data. The more categories present the less important
the need to transform to the underlying scale. I have not
introduced multple threshold models into ASREML largely becasue it is
messy and the gain is usually small.
Threhold models imply extra assumptions which usually can not be
validated with data.
So my conclusion is
Analyses of ordered categorical data as if normal is valid
and is usually quite efficient. If the data is severly skewed,
empiracal transformation may be appropriate.
Use of animal
models in binomial GLMM's sometimes give problems with the genetic component
blowing up as the effects are mapped onto an underlying scale.
It is common for 'undelying scale' estimates of heritability
to be higher than observed scale estimates becasue there is a loss
of information associated with truncating a continuous variable
to a categorical variable. However, if you ever only have the
categorical trait, then the higher value for the underlying scale
is academic.
The more data you have, the better the estimates of variance
even on the categorical scale.
In sire models, genetic correlations are generally quite consistent
between the variaous scales.
Arthur
> Thanks.
>
> Xianming
>
> ---------------------------------------------
> Xianming WEI
> CSIRO Plant Industry
> Horticultural Unit
> PMB Merbein VIC 3505
> Australia
>
> Ph: +61 3 50513170
> Fax: +61 3 50513111
> --------------------------------------------
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Arthur Gilmour PhD mailto:Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899
NSW Agriculture <61> 2 6391 3922
Orange Agricultural Institute telephone work: <61> 2 6391 3815
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