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Build the generator matrix of a continuous-time Markov chain

generator.Rd

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.

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.

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.

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))
#>            S1         S2
#> S1 -0.3678794  0.3678794
#> S2  0.3678794 -0.3678794
# 3 states: 6 free off-diagonal elements
generator(rep(-2, 6))
#>            S1         S2         S3
#> S1 -0.2706706  0.1353353  0.1353353
#> S2  0.1353353 -0.2706706  0.1353353
#> S3  0.1353353  0.1353353 -0.2706706