Log-linear transition intensity model ($q_{rs}(t\mid z)=e^{{\theta }_0+{\theta }^{T}z(t)}$)

A positive transition intensity can be modeled as $q_{rs}(t\mid z)=\exp ({\theta }_0+{\theta }^{T}z(t))$. A unit increase in a fixed covariate multiplies the intensity by $e^{{\theta }_j}$. A changing covariate generally gives a time-dependent generator matrix.