On Fri, 7 Apr 2000, Renaud Lancelot wrote:
> I am modelling liveweight growth in sheep. My dataset has many
> individuals ( > 1000) but few observations per sheep (1 to 6,
> mean ~ 5), limited to early growth (0 - 3 mo), at regular time
> intervals (15 d). I have fitted a linear mixed effects model
> (Y = XB + ZU + E), where growth was modelled by a quadratic
> function of age for fixed and random effects structures.
If I were doing it, I'd try modelling age as an exponential growth
curve rather than as a quadratic. With so few observations per
individual, probably the difference in fit between the two models
would not be detectable, and the exponential has the advantage that
there are theoretical reasons in its favor (early in the life of an
organism, at any rate) whereas power functions of any kind are purely
empirical. It also readily produces a measure of "doubling time"
(analogous to "half-life" when the exponent is negative instead of
positive), which may be of some interest and use. The general form is
Y = a exp(bX) and taking natural logs one has
log(Y) = log(a) + bX where X = age.
It wouldn't surprise me if the logarithmic transformation had a
salutary effect on the heteroscedasticity you report, as well.
You mention covariates. It may be sensible to model them as part of
the exponent, which would then look like a linear combination of X
and assorted covariates (that would seem to be easiest: you end up
with a multiple linear regression on log(Y)). If you feel compelled
to model them as linear in Y rather than in log(Y), things get rather
more complicated...
> There are evidences of both residuals serial correlation and residuals
> heteroscedasticty. Serial autocorrelation was modelled with an AR(1)
> structure. Heteroscedasticity was modelled with a power function of
> age: s2(age) = age^(2*t), where t is the variance function
> coefficient.
>
> I want to predict individual values (in fact, missing values, always
> in the range of observed covariates). With the software I am currently
> using (S+, library nlme), I can predict population values and BLUPs,
> but I would like to take into account serial correlation and
> heteroscedasticity. I am aware of methods for serial correlation
> alone, but how to deal with concomitant heteroscedasticty ?
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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