From: Suresh Krishna <[EMAIL PROTECTED]>
Subject: [R] comparing predicted sequence A'(t) to observed sequence
A(t)
To: r-help@stat.math.ethz.ch
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Hi,
I have a question that I have not been succesful in finding a definitive
answer to; and I was hoping someone here could give me some pointers to
the right place in the literature.
A. We have 4 sets of data, A(t), B(t), C(t), and D(t). Each of these
consists of a series of counts obtained in sequential time-intervals: so
for example, A(t) would be something like:
Count A(t): 25, 28, 26, 34 ......
Time (ms): 0-10, 10-20, 20-30, 30-40 .......
Each count in the series A(t) is obtained by summing the total number of
observed counts over multiple (say 50), independent repetitions of that
time-series. These counts are generally known to be Poisson distributed,
and the 4 processes A(t), B(t), C(t) and D(t) are independent of each
other.
B. It appears on visual observation that the following relationship
holds; and such a relationship would also be expected on mechanistic
considerations.
A(t) = B(t) + C(t) - D(t)
We now want to test this hypothesis statistically.
Because successive counts in the sequence are likely to be correlated,
isnt it true that none of these methods are valid ? Perhaps for other
reasons as well ?
a)Doing a chi-squared test to see if the predicted curve for A(t)
deviates significantly from the observed A(t); this also seems to not
take the variability of the predicted curve into account.
b)Doing a regression of the predicted values of A(t) against the actual
values of A(t) and checking for deviations of slope from 1 and intercept
from 0 ? Here, in addition to lack of independence, the fact that
X-values are not fixed (i.e. are variable) and the fact that X and Y are
Poisson distributed counts should also be taken into account, right ?
I would be very grateful if someone could point me to methods to handle
this kind of situation, or where to look for them. Is there something in
the time-series literature, for instance ?
