Poisson IRR value changes massively after dividing independent variable by 100

[Clark Easley]

Hello,

I am running this Poisson regression in Stata 17:

poisson num_collisions perc_complete_shapeLength LAmetro_trip_frequency precip_accum_24_hour_mm_sq i.season,irr vce(robust)

Quick variable descriptions:

num_collisions = number of cycling collisions on a given day within the area I am studying
perc_complete_shapeLength = the percentage completion of cycling lanes being painted within the same area (this is my main variable of interest)
LAmetro_trip_frequency = the number of daily metro bike share trips, used as a proxy for overall cycling ridership
precip_accum_24_hour_mm_sq = squared mm of daily rain
i.season = seasonal indicator

When I run this regression using the perc_complete_shapeLength as measured from 0-100, I get an IRR value of .9959869.
I figured I would see what were to happen if I scaled the percentage from 0-1, by dividing the variable by 100. To my surprise, the IRR value changed to .668905. All the other IRR values remained exactly the same, as well as the p values.

Does anyone know why this would be?

Also- I am still a bit confused on how to interpret these IRR values if anyone has advice on that.

All the best,
Clark

[Maarten Buis]

IRR is multiplicative, so if you change the scale by dividing by 100, then the IRR changes IRR^100, and 0.9959869^100=0.6689

[Clark Easley]

Thank you for the response!

In the case that I use the IRR of 0.9959869, how would I interpret a one unit increase in the percentage of the bike lanes being painted? Or would the one unit increase be from 0 to 100%?

[Maarten Buis]

If the percentage of cycling lanes painted increases by 1 percentage point, the number of cycling collisions decreases by (0.996-1)*100=-0.4%

If the percentage of cycling lanes painted changes from 0 to a 100%, the number of cycling collisions decreases by (0.669-1)*100=-33.1%

If the percentage of cycling lanes painted increases by 10 percentage points, the number of cycling collisions decreases by (0.9959869^10-1)*100=-3.9%

I would probably prefer the last interpretation, though all three are mathematically equivalent.