Transition intensity ($q_{rs}(t)$)

The transition intensity $q_{rs}(t)$ is the instantaneous rate of moving from state $r$ to state $s$, conditional on occupying state $r$ immediately before time $t$.

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.