Struggling to make sense of coefficients in production-constrained spatial interaction model (Poisson) I'm having a hard time trying to understand what is the meaning of the coefficients of a production-constrained spatial interaction model re-specified as a Poisson linear regression model.
Following this guide to run a production-constrained spatial interaction model (section 2):
https://rpubs.com/adam_dennett/376877
Which is the practical part of this paper:
https://www.australianpopulationstudies.org/index.php/aps/article/view/38
The model is re-specified as a Poisson regression model.
Here's the output of the model in the guide.

I suppose that those coefficients can't be interpreted as in a linear regression, because the whole equation ins exponentiated.
Thanks in advance, any feedback will be highly appreciated.
 A: It can be interpreted the same way as linear regression except for the log (conditional) average number of counts (or what ever your outcome is). Alternatively, you can interpret the exponential of the coefficient as the multiplicate increase in the expected number of counts if you increase the covariate associated with the coefficient by a single unit. This is true because the Poisson model is of the form:
$$E[Y|X_1, X_2, X_3] = \exp \left\{aX_1 + bX_2 + c X_3 \right\} $$
and thus:
$$E[Y|X_1 + 1, X_2, X_3] = \exp \left\{a(X_1+1) + bX_2 + c X_3 \right\}$$
$$ = \exp \left\{a \right\} \exp \left\{ aX_1 +  bX_2 + c X_3 \right\} $$
$$= \exp \left\{a \right\}E[Y|X_1, X_2, X_3].$$
So,
$$\exp \left\{a \right\} = \frac{E[Y|X_1 + 1, X_2, X_3]}{E[Y|X_1 , X_2, X_3]}$$
You can also show
$$\frac{d}{dx} \frac{E[Y|X_1 + x, X_2, X_3]}{E[Y|X_1 , X_2, X_3]} \big |_{x=0} = \exp \left\{a \right\},$$
or
$$ \frac{E[Y|X_1 + dx, X_2, X_3]}{E[Y|X_1 , X_2, X_3]} \approx \exp \left\{a \right\} dx,$$
which can be interpreted as the incremental multiplicative change in the expected count.
