Hidden semi-Markov models (HSMMs) are a flexible extension of HMMs. For direct numerical maximum likelhood estimation, HSMMs can be represented as HMMs on an enlarged state space (of size
This function computes the transition matrices of a periodically inhomogeneos HSMMs.
tpm_phsmm(omega, dm, eps = 1e-10)list of dimension length L, containing sparse extended-state-space transition probability matrices of the approximating HMM for each time point of the cycle.
embedded transition probability matrix
Either a matrix of dimension c(N,N) for homogeneous conditional transition probabilities (as computed by tpm_emb), or an array of dimension c(N,N,L) for inhomogeneous conditional transition probabilities (as computed by tpm_emb_g).
state dwell-time distributions arranged in a list of length N
Each list element needs to be a matrix of dimension c(L, N_i), where each row t is the (approximate) probability mass function of state i at time t.
rounding value: If an entry of the transition probabily matrix is smaller, than it is rounded to zero. Usually, this should not be changed.
N = 2 # number of states
L = 24 # cycle length
# time-varying mean dwell times
Z = trigBasisExp(1:L) # trigonometric basis functions design matrix
beta = matrix(c(2, 2, 0.1, -0.1, -0.2, 0.2), nrow = 2)
Lambda = exp(cbind(1, Z) %*% t(beta))
sizes = c(20, 20) # approximating chain with 40 states
# state dwell-time distributions
dm = lapply(1:N, function(i) sapply(1:sizes[i]-1, dpois, lambda = Lambda[,i]))
## homogeneous conditional transition probabilites
# diagonal elements are zero, rowsums are one
omega = matrix(c(0,1,1,0), nrow = N, byrow = TRUE)
# calculating extended-state-space t.p.m.s
Gamma = tpm_phsmm(omega, dm)
## inhomogeneous conditional transition probabilites
# omega can be an array
omega = array(omega, dim = c(N,N,L))
# calculating extended-state-space t.p.m.s
Gamma = tpm_phsmm(omega, dm)
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