The optimization algorithm used in nlme does not allow constraints on
the coefficients in the model. You can, however, reparameterize your
model in such a way that the constraints are satisfied within an
unrestricted optimization framework. For example, if you re-express
your asymptote as
a = 100/(1+exp(-A))
then A is unrestricted, while 0 < a < 100. In this case, a is a
monotonically increasing function of A and you can derive confidence
intervals for a from the confidence intervals obtained for A (and the
confidence intervals for a are guaranteed to be contained in (0,100)).
You can also assign a random effect to A and still guarantee that the
resulting a will be in the desired range. So, your model would look
something like
y ~ 100 * (1 - exp(-b * x))/(1 + exp(-A)))
after the reparameterization.
Hope this helps,
--Jose'
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Jose' Pinheiro
Bell Laboratories jcp@research.bell-labs.com
600 Mountain Avenue, Room 2C-258 office: (908) 582-2390
Murray Hill, NJ 07974 fax: (908) 582-3340
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