Dear R users,
I have a Coxian Phase type Generator Matrix (Continuous time Markov chain) that
I am trying to estimate the
parameters via a Maximum Likelihood Estimation (MLE). However this markov chain
can be from 2 by 2 to 6 by 6.
Given initial set of parameters (theta), and the size of the matrix say n = 3 (3
* 3 matrix), I want to construct a for loop (or if there is something more
sophisticated) that can return combination of matrices from my initial
parameters.
Here is an example: #This set of code cannot be compiled in R - It is for
illustrative purposes#
if (n = 3){ # 3 by 3 matrix
theta=c(lambda1, lambda2, mu2, mu3) # my set of parameters
>From this set of parameters, I would like the following matrices:
M = [-lambda1-mu1, lambda1, 0
0, -lambda2, lambda2
0, 0, -mu3]
and
M = [-lambda1, lambda1, 0
0, -lambda2-mu2, lambda2
0, 0, -mu3]
}
if (n = 4){ #4 by 4 matrix
theta=c(lambda1, lambda2, lambda3, mu2, mu3)
M = [-lambda1-mu1, lambda1, 0, 0
0, -lambda2, lambda2, 0
0, 0, -lambda3, lambda3]
0, 0, 0, -mu3]
and
M = [-lambda1, lambda1, 0, 0
0, -lambda2-mu2, lambda2, 0
0, 0, -lambda3, lambda3]
0, 0, 0, -mu3]
and
M = [-lambda1, lambda1, 0, 0
0, -lambda2, lambda2, 0
0, 0, -lambda3-mu2, lambda3]
0, 0, 0, -mu3]
}
As the number of parameters increase, the combination of matrices will also
increase.
Is there a way of constructing such a loop, giving initial set of parameters,
that can list SPECIFIC combination of matrices which can be incoorporated in to
MLE.
Thank you all
Eren Demir