The first thought which came to mind when I read the description of
your problem was that the heteroskedasticity could be dealt with if
you employed a local nugget effect using a power of the mean. Of
course, in addition to the heteroskedasticity, you have to account
for the within animal correlation structure. Since the measurements
are unequally spaced, a spatial covariance structure would seem
appropriate. What I don't know is whether you can combine the two
options local(mean) and sp(pow)(age). I would think that might not
work. Have you considered a model for log(weight). If the variance
is proportional to the mean, then log(weight) should have constant
variance. Then all you would need to be concerned with is the
within animal correlation structure. For that you could use the
spatial covariance structure. Of course, if weight increased
linearly with age, then log(weight) would not increase linearly with
age. You probably want to work with the functional form in which
the expectation is modeled appropriately whether that be employing
weight or log(weight) as the response.
You could employ a weighted regression model employing weight 1/age
to account for the heteroskedasticity. But that assumes that the
variance does increase linearly with age. Is that in fact true? If
the variance increases linearly with weight (such that a POM variance
structure was appropriate) then weight would have to increase linearly
with age alone (or at least age would have to be the dominant term
affecting weight). How does animal gender affect animal weight?
If animal gender has an effect on weight, then you might be
misspecifying the variance structure if you only employ 1/age as
a weight variable.
Here is a thought. How about weighting by the expected value of
the mean using an iterative approach like that for the POM analysis?
Initialize the weight variable to be 1/<animal weight>. Fit your
regression model employing weight statement and spatial covariance
structure and then compute expected animal weight. Update the
weighting variable to be 1/<expected animal weight>. Keep iterating
until some measure of convergence.
I do really think that you are on the right track. It is just that
you do need to consider how the heteroskedasticity and correlation
structures can be handled simultaneously.
--- JoŽl_Rivest <jrivest@CDPQINC.QC.CA> wrote:
> Apology for my english writing. Hope I will be clear enough ;)
> I have repeated measures of weight on some 350 animals. I want to
> investigate the effet of two factors, sex and breed, on the growth
> curve. Random effects as pen, litter, sire, are specified in a random
> statement. I want to modelise the effect of age on the weigth by a
> Some animals has 5 weight measures, others 6, 7, 8 or 9. These
> measures are unequally spaced. Moreover the weight's variance shows a
> signicant heteroscedasticity. I would like to have opinion about the
> following possibilities and any relevant suggestions. The analysis
> will be performed with Proc Mixed.
> - The covariance structure is modelled by using the SP(POW) structure
> repeated ageclass /type=sp(pow) (age) sub=animal;
> In that case, should I include lines with missing values for animals
> having not 9 measures of weight?
> That structure allows to analyse unequally spaced repeated measures,
> but not to modeled heteroscedasticity.
> - The heteroscedasticity could be considered by specifying a WEIGHT
> statement :
> WEIGHT ageinv;
> where ageinv is equal to 1/age;
> - The heteroscedasticity could be considered by including a second
> REPEATED statement to represent the variance as a power of the mean :
> repeated /local=pom(mean)
> In that last case, the steps suggested in "Sas system for mixed
> models, p.279" should be followed.
> Any relevant comment of suggestion will be appreciate.
> JoŽl Rivest
Fred Hutchinson Cancer Research Center
Ph: (206) 667-2926
Fax: (206) 667-5977
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