How to interpret coefficients obtained with the "poisson" command ?

[Ive Muller]

Hello,

I am currently studying the correlation between the number of universities each country has in the top 500 of the QS university ranking (dependant variable) and academic freedom (independant variable).

Since I use count data, I decided to do a Poisson regression with the help of the

poisson

command.

Here are my results :

"v2xca_academ" is the coeffient of academic freedom, while "Log_PIB_hab" is the coefficient for Log GDP per capita, used as a control variable.

How would I interpret these coefficients ? I tried to look it up on the internet, but I get contradicting answers (some sources tell me take the exponential of my coefficient, others tell me to interpret the coefficient in percentages), so I'm not really sure how to read these results.

[Ken Chui]

See examples 1 and 2 in https://www.stata.com/manuals/rpoisson.pdf

See this other annotated output on https://stats.oarc.ucla.edu/stata/ou...on-regression/

Also, look into a concept called "offset". This model currently has problem because the counts of university is also related to how big a country is. In a rather bad analogy, you're comparing if the number of fleas in a hamster and the number of fleas in a moose are the same. The moose is likely going carry more fleas simply just because it's larger.

[Ive Muller]

This model currently has problem because the counts of university is also related to how big a country is. In a rather bad analogy, you're comparing if the number of fleas in a hamster and the number of fleas in a moose are the same. The moose is likely going carry more fleas simply just because it's larger.

In other regressions of this model, I control for log of population. Does this take care of the problem ?

Another solution I saw (in the paper "University rankings game and its relation to GDP per capita and GDP growth" by C Tan Kuan Lu) would be to have "universities per capita" as a dependant variable (simply dividing the number of universities by population). Could this also be a solution, or does it create new problems ?

[Ken Chui]

You have the raw data. Why not try all these models and see which approach recovers the hand calculated rate?

Example:

clear
input str3 country pop univ x
A 1200 12 1
B 1000 15 1
C  800  6 1
D 9000 32 0
E 2300 17 0
F 1000 11 0
end
gen lnpop = log(pop)
gen upop  = univ / pop

*---------
* Let's check the true rate ratio:
preserve
collapse (sum) pop univ, by(x)
gen rt1 = univ / pop
display = rt1[2] / rt1[1]
restore

*---------
* Without offset approach:
poisson univ x, irr

* With offset:
poisson univ x, irr exposure(pop)

* Adjust for log(pop)
poisson univ x lnpop, irr

* Use unversity/pop as dependent
poisson upop x, irr