 Solution

Preserve the original row order and set $G_i=0$ for the first eight fixed-route providers and $G_i=1$ for the twelve on-demand providers. A suitable group comparison builds on a selected small predictor set $z_i$:The model with $\gamma =0,\delta =0$ pools service types; adding $\gamma$ changes the baseline; adding selected components of $\delta$ allows different predictor dependence. Center $z$ at meaningful values so that $e^{\gamma }$ compares groups at those values. The predictor-specific rate ratio is $e^{{\beta }_j}$ in the fixed-route group and $e^{{\beta }_j+{\delta }_j}$ in the on-demand group; the group ratio at predictor value $z$ is $e^{\gamma +z^T\delta }$.

Fit common-slope and selected-interaction models, respecting model hierarchy by retaining corresponding main effects. Test the added interaction block jointly with a likelihood-ratio test, or an appropriate quasi-likelihood comparison under estimated dispersion, and check group-specific residual patterns and leave-one-provider sensitivity. Seven interactions plus all main effects would use 16 parameters for just twenty providers and leave only four residual degrees of freedom; an indiscriminate full interaction model is consequently a poor basis for stable inference.

The excerpt contains only $G=0$, so neither the service-type effect nor any interaction is estimable from it. Full-data estimates could distinguish a baseline difference from genuinely different slopes, but the printed records cannot establish either conclusion.