Re: Correlated repeated measurements of circular data
- From: "David Jones" <dajxxx@xxxxxxxxx>
- Date: Thu, 10 Aug 2006 17:37:43 +0100
Gerrit Eichner wrote:
Hello, everybody,several)
I have encountered repeated measurements data which are of circular
type. To be more specific, for each individual (in a group of
the exact date and time of every ventricular premature capture (VPC)am
was recorded during a long-term electrocardiograph (ECG) lasting
several
weeks. VPCs can occur repeatedly during such an ECG. In this case I
only interested in the time of the day (not the date) of every VPC.24
Consequently, the data of every individual are a random number of
repeated (and presumably correlated) measurements on the circle of
hours.and
Can anybody give me a hint where to search for the statistical
treatment
of such data. (My Google search did not bring up anything helpful.
The - very informative! - book "Directional Statistics" by Mardia
Jupp is,
as far as I could see, on independent observations only.)
An alternative possibility is to treat these events as a point process
and look for an intensity function that varies periodically (period 24
hours). Something from "labelled point processes" may help to deal
with the quantities being observed.
If you are mainly interested in modelling the "measurements" being
made (not the time), then perhaps you don't need to treat this using
"circular data" theory, but simply do some sort of regression using
time as a dependent variable by way of a pair of sine and cosine
terms.
As for your "presumably correlated" measurements, you need to think
more clearly why you think they may be correlated as this affects any
modelling. For example, "correlated because they come from the same
individual" is different from "correlated because they come from the
same individual at the same time" (random measurement errors about a
"true" value that varies randomly in time) or "correlated because they
come from the same individual at the a nearby time" (temporal
correlation of "true" value) or "correlated because they come from the
same individual at randomly selected times where there is a periodic
variation in response with time" (correlation arising from random
selection of time-points).
David Jones
.
- References:
- Correlated repeated measurements of circular data
- From: Gerrit Eichner
- Correlated repeated measurements of circular data
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