= 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 $z_i$:
$$
\boxed{\log\mu_i=\beta_0+\gamma G_i+z_i^T\beta+G_i z_i^T\delta.}
$$
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.
\b[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.
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