Build generator matrices of a continuous-time Markov chain

This function builds infinitesimal generator matrices for a continuous-time Markov chain based on a design matrix and coefficient matrix.

Usage

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

Arguments

Z

Covariate design matrix with or without intercept column, i.e. of dimension c(nObs, p) or c(nObs, p+1). If not provided, intercept column is added automatically.

beta

Matrix of coefficients for the off-diagonal elements of the generator matrix of dimension c(nStates * (nStates-1), p+1). First columns contains the intercepts.

Eta

optional pre-calculated matrix of linear predictors of dimension c(nObs, nStates * (nStates-1)). If provided, no Z and beta are necessary and will be ignored.

byrow

logical indicating if the generator matrices should be filled by row

report

logical, indicating whether the generator matrices Q should be reported from the fitted model. Defaults to TRUE, but only works if when automatic differentiation with RTMB is used.

Value

array of infinitesimal generator matrices of dimension c(nStates, nStates, nObs)

Details

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

See also

Other transition probability matrix functions: generator(), 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