Build the embedded transition probability matrix of an HSMM from unconstrained parameter vector
Hidden semi-Markov models are defined in terms of state durations and an embedded transition probability matrix that contains the conditional transition probabilities given that the current state is left . This matrix necessarily has diagonal entries all equal to zero as self-transitions are impossible.
This function builds such an embedded/ conditional transition probability matrix from an unconstrained parameter vector. For each row of the matrix, the inverse multinomial logistic link is applied.
For a matrix of dimension c(N,N), the number of free off-diagonal elements is N*(N-2), hence also the length of param. This means, for 2 states, the function needs to be called without any arguments, for 3-states with a vector of length 3, for 4 states with a vector of length 8, etc.
Compatible with automatic differentiation by RTMB
tpm_emb(param = NULL)
param: unconstrained parameter vector of length N*(N-2) where N is the number of states of the Markov chain
If the function is called without param, it will return the conditional transition probability matrix for a 2-state HSMM, which is fixed with 0 diagonal entries and off-diagonal entries equal to 1.
embedded/ conditional transition probability matrix of dimension c(N,N)
# 2 states: no free off-diagonal elements omega = tpm_emb() # 3 states: 3 free off-diagonal elements param = rep(0, 3) omega = tpm_emb(param) # 4 states: 8 free off-diagonal elements param = rep(0, 8) omega = tpm_emb(param)
Other transition probability matrix functions: generator(), tpm(), tpm_cont(), tpm_emb_g(), tpm_g(), tpm_p()