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 Z has only p columns, an 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). The first column 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; if TRUE (default), the coefficient matrix beta is reported from the fitted model. Requires automatic differentiation with RTMB.

Value

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

Details

Deprecated: please use generator(beta, Z) for all model types instead.

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