generator: Build the generator matrix of a continuous-time Markov chain

In LaMa: Fast Numerical Maximum Likelihood Estimation for Latent Markov Models

Build the generator matrix of a continuous-time Markov chain

Description

This function builds the infinitesimal generator matrix for a continuous-time Markov chain from an unconstrained parameter vector.

Usage

generator(
  beta,
  Z = NULL,
  Eta = NULL,
  byrow = FALSE,
  report = TRUE,
  param = NULL
)

Arguments

beta	parameters; either a vector of length nStates * (nStates-1), or a matrix of dimension c(nStates * (nStates-1), p+1) if design matrix Z is also provided.
Z	optional covariate design matrix with or without intercept column, i.e. of dimension c(nObs, p) or c(nObs, p+1). If provided, beta needs to be a matrix of dimension c(nStates * (nStates-1), p+1).
Eta	optional pre-calculated matrix of linear predictors of dimension c(nObs, nStates * (nStates-1)). If provided, Z and beta will be ignored.
byrow	logical indicating if the generator matrix should be filled by row
report	logical, indicating whether the generator matrix Q should be reported from the fitted model. Defaults to TRUE, but only works if when automatic differentiation with RTMB is used.
param	depricated, please use argument beta instead.

Details

Off-diagonal entries are calculated as \exp(\beta_i) to ensure positivity. The diagonal entries are then set to the negative row sums, which is required for generator matrices.

If a design matrix Z or a matrix of linear predictors Eta is provided, the function will automatically call generator_g to build the generator matrix based on the design matrix and coefficient matrix. In that case, the argument beta needs to be a matrix of coefficients of dimension c(nStates * (nStates-1), p+1), where the first column contains the intercepts.

Value

infinitesimal generator matrix of dimension c(nStates, nStates) or array of such matrices of dimension c(nStates, nStates, nObs) if Z or Eta is provided.

See Also

Other transition probability matrix functions: generator_g(), tpm(), tpm_ct(), tpm_emb(), tpm_emb_g(), tpm_g(), tpm_g2(), tpm_p()

Examples

# 2 states: 2 free off-diagonal elements
generator(rep(-1, 2))
# 3 states: 6 free off-diagonal elements
generator(rep(-2, 6))

LaMa documentation built on July 25, 2026, 1:08 a.m.