We have studied finite Markov Chain elaborately with almost all its
properties. One of the main issues of Markov Chain is the
estimation procedure of the transition probabilities. In this study
we restrict our self in the most popular estimation procedure and
that is the Maximum Likelihood Estimation (MLE) procedure. Here in
this study we have also considered two efficient and mostly used
test procedures for indentifying the properties of Markov Chain and
they are order test and the test of homogeneity or stationarity
test. And we apply these estimation procedure and the test
procedures to the diabetes mellitus data which is the most popular
repeated ordinal data. And our findings of applying these
procedures (estimation procedure and the test procedures) over the
data is that the diabetes mellitus data follows the second order
Markov Chain and time homogeneous property. And we also proposed
logistic regression model for each consecutive visit.
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