On 06-Aug-07 19:26:59, lamack lamack wrote:> Dear all, I have a factorial design where the
> response is an ordered categorical response.
>
> treatment (two levels: 1 and 2)
> time (four levels: 30, 60,90 and 120)
> ordered response (0,1,2,3)
>
> could someone suggest a correct analysis or some references?
For your data below, I would be inclined to start from here,
which gives the counts for the different responses:
Response
--------------------
Trt Time 0 1 2 3
--------+--------------------+----
Tr1 30 | 1 3 | 4
60 | 2 1 1 | 4
90 | 3 1 | 4
120 | 3 1 | 4
--------+--------------------+---
Tr2 30 | 2 2 | 4
60 | 3 1 | 4
90 | 3 1 | 4
120 | 1 2 1 | 4
================================Tr1 | 0 9 3 4 | 16
--------+--------------------+---
Tr2 | 1 10 2 3 | 16
================================
This suggests that, if anything is happening there at all,
it is a tendency for high response to occur at shorter times,
and low response at longer times, with little if any difference
between the treatments.
To approach this formally, I would consider adopting a
"re-randomisation" approach, re-allocating the outcomes at
random in such a way as to preserve the marginal totals,
and evaluating a statistic T, defined in terms of the counts
and such as to be sensitive to the kind of effect you seek.
Then situate the value of T obtained from the above counts
within the distribution of T obtained by this re-randomisation.
There must be, somewhere in R, routines which can perform this
kind of constrained re-randomisation,but I'm not sufficiently
familiar with that area of R to know for sure about them.
I hope other readers who know about this area in R can come
up with suggestions!
best wishes,
Ted.
> subject treatment time response
> 1 1 30 3
> 2 1 30 3
> 3 1 30 1
> 4 1 30 3
> 5 1 60 3
> 6 1 60 1
> 7 1 60 1
> 8 1 60 2
> 9 1 90 2
> 10 1 90 1
> 11 1 90 1
> 12 1 90 1
> 13 1 120 2
> 14 1 120 1
> 15 1 120 1
> 16 1 120 1
> 17 2 30 3
> 18 2 30 3
> 19 2 30 1
> 20 2 30 1
> 21 2 60 1
> 22 2 60 2
> 23 2 60 1
> 24 2 60 1
> 25 2 90 1
> 26 2 90 1
> 27 2 90 1
> 28 2 90 3
> 29 2 120 1
> 30 2 120 2
> 31 2 120 0
> 32 2 120 1
>
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E-Mail: (Ted Harding) <ted.harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 07-Aug-07 Time: 00:30:19
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