In article <gL2M8.12479$[EMAIL PROTECTED]>,
Jun Dong <[EMAIL PROTECTED]> wrote:
>Hi, all,
>I currently have a data set about discrete Markov Chain.
>1000 patients can be in 6 ordinal status, named 1 to 6. We observed
>the status of each patient at time 0, 18 month, and 36 month. i.e. 3
>time
>points. We assume the change of status in this population follows a
>stationary MC process. From time 0 to 18 and from time 18 to 36
>now have the same transition probability matrix P (by assumption).
>>From what we observed from the data, we can construct the
>empirical transition probability matrices, because we know exactly
>the status for each patient and thus the proportion of changes.
>Now, I need an official method to estimate the common P mentioned
>above, best a method in the literature. Or please give me a reference
>that I can look up.
Just combine the data. The likelihood function is
\prod p_{ij}^{n_{ij}},
where p_{ij} is the probability that an individual in state
i will move to state j, and n_{ij} is the number who do it.
So the maximum likelihood estimate of p_{ij} is just the
sample proportion n_{ij}/\sum_k n_{ik}.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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