[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
st: Modelling the variance structure.
I'm looking at Rabe-Hesketh and Skrondal's book "Multilevel and Longitudinal
Modeling Using Stata". They examine the random intercept model
y[i,j] = (beta + zeta[1,j]) + (beta + zeta[2,j])x[i,j] + epsilon[i,j]
where "i" indexes an observation in subject "j", the betas are constants,
the zetas are the random components of the (random) coefficients and epsilon
is simply random variation. "y" is the Graduate Certificate of Secondary
Education score and "x" is the score on the London Reading Test (Chapter 3,
for those who have the book).
Simple algebra leads to the conclusion that
var(y|x) = psi[1,1] + 2psi[1,2]x + psi[2,2]x^2 + theta
where psi[1,1] is the variance of zeta, psi[2,2] is the variance of
zeta and psi[1,2] is their covariance and theta is the random variation.
Given that psi[2,2] is a variance (and hence positive), the variance
structure is convex in x with higher values of the variance at the extremes
of x and lower in the middle (depending, of course, on the range of x in the
analysis). However, there will be situations in which, based on
clinical/practical considerations, it would be expected that variance
function would be concave (i.e. lower at the extremes and higher in the
middle). For example, I'm looking at the level of a certain hormone
(Inhibin-B) in women in the follicular phase of their menstrual cycle. Based
purely on clinical considerations, both the mean and variance are expected
to be lower at both the beginning and end of this phase than in the middle
of the phase. The data indicate that this is in fact the case.
So my question is, how can I best explicitly model the variance structure in
STATA to reflect the clinical process? I'm using STATA 9.
Thanks to all who respond.
Hotmail en Messenger on the move http://www.msn.nl/services
* For searches and help try: