 Solution

The linear predictor is unchanged by ${\alpha }_j\mapsto {\alpha }_j+c$, ${\beta }_t\mapsto {\beta }_t+d$, $\mu \mapsto \mu -c-d$. Without constraints, different parameter triples therefore give the same rates and likelihood. Identifiability requires choosing one representative of this redundancy.

Taking the first levels as reference yields ${\alpha }_1={\beta }_1=0$. ThenThese identify all three free parameters, while ${\lambda }_{22}={\lambda }_{21}{\lambda }_{12}/{\lambda }_{11}$ is the model's no-interaction constraint. The zero reference effects fix a parametrization; they do not remove the baseline rate or impose equal rates across groups.