[R-sig-dyn-mod] Help to fit a dynamic model - irregular time

[Setzer.Woodrow at epamail.epa.gov]

Dr. Tura,
I wonder if you need to specify the model a little more clearly.  As
written, A() is an unknown function such that A(t+1) - A(t) = b +
Error2.  But, you have times on a finer time scale, since the first
three times do not even span the time from 0 to 1.  Your model does not
give any way to interpolate to shorter time intervals.
I can see how you might modify the recursion for A() to small time
increment dt (A(t + dt) ~ A(t) + b*dt + Error2), but it is not so clear
how rate should change over a short interval.
Maybe something like:

log(rate(t+dt)) - log(rate(t))= log(A(t))*dt + log(Error1)

When dt = 1, this gives you the expression you gave us.

You need to decide how or whether the error variances should depend on
time, too.  If they are the result of some process that you are thinking
of as stochastic, then the variance probably depends on the time
interval.

You also need to tell us what A(0) ought to be, though I guess that
could be estimated, also.

Woody

R. Woodrow Setzer, Ph. D.
National Center for Computational Toxicology
http://www.epa.gov/comptox
US Environmental Protection Agency
Mail Drop B205-01/US EPA/RTP, NC 27711
Ph: (919) 541-0128    Fax: (919) 541-1194

r-sig-dynamic-models-bounces at r-project.org wrote on 12/09/2009 03:46:55
AM:

> [R-sig-dyn-mod] Help to fit a dynamic model - irregular time
>
> Bernardo Rangel Tura
>
> to:
>
> r-sig-dynamic-models
>
> 12/09/2009 03:48 AM
>
> Sent by:
>
> r-sig-dynamic-models-bounces at r-project.org
>
> Please respond to Special Interest Group for Dynamic Simulation Models
in R
>
>
> Hi R-masters
>
>
> I need help to fit a dynamic model. In my assumption the model is
>
> rate(t+1) ~ A(t)*rate(t)*Error1
> A(t+1) ~ A(t) + b + Error2
>
> In attached file I put my 45 points of information, but the time of
> observation is irregular. Look the 3 initial observations
>
> time
> rate
>                                 0.16
>                                 0.09
>                                 0.25
>                                 0.23
>                                 0.38
>                                 0.28
>
>
> Is possible fit this model?
>
>
> --
> Bernardo Rangel Tura, M.D,MPH,Ph.D
> National Institute of Cardiology
> Brazil
> [attachment "data.csv" deleted by Woodrow Setzer/RTP/USEPA/US]
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