Coefficients of Poisson Regression unexplainable low

[Florian12345]

Hi all,

first and foremost, any help for my little issue here is much appreciated!

I am currently writing my master thesis, where I'm analyzing common currency effects on trade flows. Therefore, I'm using the Gravity Model of Trade with panel data. After conducting a first OLS regression with rather unsatisfactory results (due to heteroskedasticity), I performed a GLS regression, which was a big improvement. Subsequently, I applied a Poisson Quasi Maximum Likelihood to the same data, however, even though most coefficients are statistically significant, the values are extremely small (as compared to the coefficient values I obtained from my previous regressions). A rough estimate would be that they are 1/25 of the former ones; the signs of the coefficients are the same however. Unfortunately, this is the case for different poisson analyses I applied to it, such as ppml, poisson, or xtpoisson.

I simply cannot find an explanation for that, especially because PQML is according to various scholars an excellent method for the gravity model.


I am using Stata 12; my coefficients are never exceeding 0.02 (a rough average of the values I obtained from my other regression analyses was +/-0.5)

I was wondering if I maybe did something wrong, or if anyone has an explanation for my problem?

Thanks a lot!!

[Florian12345]

I thought that an image of my output might help

[Rich Goldstein]

I think you are forgetting the interpretations of the coefficients; for OLS, it is additive (say, e.g., you have only a constant and the one predictor; to obtain predicted values you add the value of the coefficient (times the value of the variable) to the constant; for Poisson, the effect is multiplicative: you multiply the value of the coefficient (times the value of the variable) by the constant

try the following:

sysuse auto, clear
ta foreign, su(gear)
regress gear foreign
poisson gear foreign, nolog
di exp(_b[_cons]) * exp(_b[foreign])

compare the results to what you found in the -tabulate- command

[Florian12345]

Thank you very much for your wonderful example; it has helped me a lot already! Until not too long ago, I didn't know anything about statistics at all, that's why I will have to ask you this (probably rather stupid question):

I understand that the '3.5072727' from below is the 0.7007343 + 2.806538 in the OLS, but if I multiply the coefficient of the Poisson output (0.2228869) with its constant (1.031952) it doesn't add up to '3.5072727'; I feel pretty dumb for asking this question, because you have basically provided me the answer in your post already.

. di exp(_b[_cons]) * exp(_b[foreign])
3.5072727


Also, I was wondering why the Pseudo R2 seems to be really low in Poisson Regression Analyses; it seems to be a value on which I shouldn't place too much attention to, right?

Edit: And is there maybe a common way how to compare the coefficients of Poisson analyses with those of OLS? Do I have to just multiply them with the constants and compare it with the OLS coefficients to which I added the constant?

[daniel klein]

Please provide references for cross-posting at Stata-Forum.de in both forums. Here at Statalist you are explicitly asked to do so per FAQs, which you are supposed to read before posting.

Also note that it is appreciated by many users if you register with your full real name (also explained in the FAQs).

As to your remaining questions, a missing value for the pseudo-R might (but need not) be a sign that there is something wrong. I cannot say much more at this point.

Whether it makes sense at all to compare coefficients from a linear OLS Model to those obtained by the poisson model, I cannot say, but I would ask myself what kind of question I would like to answer by such a comparison.

Best
Daniel

[Florian12345]

I'm sorry for the violation, I should have indeed read the FAQ more carefully prior to posting. In general, I would like to keep my exposure as little as possible, that's why I didn't sign up with my full name.

Thanks again for your help though!

I would like to compare my OLS to my PPML in a similar fashion to the screenshot that is attached to this post, and was wondering what the best possibility for that would be. This is pretty much to what my question(s) come down.

Thank you very much,

Florian

[Nick Cox]

Also cross-posted at http://www.talkstats.com/showthread....GLS-OLS-output)

[Martin Bresslein]

Read the following page if you have not done so yet:
http://privatewww.essex.ac.uk/~jmcss/LGW.html
One thing I could imagine is that you used trade in logs where with PPML - or PQML as you call it - trade should be used in levels. Apart from that, without providing more information - code, variables used, functional form etc. - it is quite hard to point to something...

[Jeff Wooldridge]

Florian: I strongly suspect you did what Martin said: you are using log(trade) in the Poisson regression, when it should be the level of trade. Use a linear model with ln(trade) or an exponential model with trade.

[Florian12345]

Wow, that was it! Thanks a lot, I now got the results I was hoping for! Your help was much appreciated!!