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Build the embedded transition probability matrix of an HSMM from unconstrained parameter vector

tpm_emb.Rd

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

Usage

tpm_emb(param = NULL)

Arguments

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.

Value

embedded/ conditional transition probability matrix of dimension c(N,N)

See also

Other transition probability matrix functions: generator(), tpm(), tpm_cont(), tpm_emb_g(), tpm_g(), tpm_p()

Examples

# 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)