mepoisson marginsplot: problems with marginsplot scale even after changing exposure() in model specification

[Ariela Braverman]

Hi, I'm running a mixed poisson model using mepoisson.
I'm modeling events (yrtotal) per 1000 people, and I want to get the marginsplot of the interaction.
My code runs without issues but the plot is the same when I use nt as the exposure or nt1000.
The correct model specification is with nt1000 as my outcome is rate per 1000 people.
Anyone knows why this is happening or how to go about this?
thank you

This is my code:

* Create exposure variable
* total N per year
bys measurment_yr: gen nt = _N
* divide by 1000 to get the correct offset
gen nt1000 = nt/1000

* Crude model
mepoisson yrtotal i.population##c.measurement_yr, ///
exposure(nt1000) || new_id:, irr
* Estimate marginal effects for the interaction
margins population, at(measurement_yr = (0(1)2))
* Plot marginal effects 
marginsplot, plotopts(msize(*0.65)) ///
ytitle("Visits per 1000 clients") ///
title("Crude model") ///
xtitle("") ///
legend(rows(1) cols(2) size(small)) ///
name(EDU_AE_crude_`lv'100, replace)

[Andrew Musau]

Including an exposure variable in mepoisson or poisson just results in the logarithm of this variable being included In the RHS with the constraint that its coefficient equals 1. So dividing this variable by 1000 is the same as taking away a constant ln(1000) from the logarithm, from the properties of logarithms. The only effect is that the constant term in the estimation changes. Note that:

$$ln \left(\frac{x}{y} \right)= ln(x)- ln(y) \Rightarrow ln \left(\frac{x}{1000}\right) = ln(x)- ln(1000).$$

In your case, it appears all you want to do is to rescale the y-axis of the marginsplot. You can do this directly on the plot, or just specify this within the -expression()- option of margins.

margins population, at(measurement_yr = (0(1)2)) expression(predict()*0.001)