coefficients in count data model

[Simona Gamba]

Hi all.
I have a count data model (in particular, a NB model), and I am asking stata to show me the IRR.
What I get, are some strange coefficients.

In particular, the constant is significant but equal to 4e-33 (in IRR). I was checking on the internet to understand if this was common, and what I found in the examples (http://www.ats.ucla.edu/stat/stata/dae/nbreg.htm; http://www.ats.ucla.edu/stat/stata/dae/poissonreg.htm) is that, when IRR are shown, the value of the contant is never shown (although the model was estimated with the constant).
Do you know why the value of the constant is not shown? It may be because there is no sense to compute the IRR of the constant? And, in this case, do I have to report its coefficient (instead of the IRR)?

The second point is that, in my model, I have some independent variables that are in log. Is this ok in count data model? I was thinking I could interprete the coefficients of these variables as the % change in the dependent variable for a 1% increase in the value of the independent variable. However, I get some crazy coefficients (like an elasticity of 48000). So I am wondering if maybe it is not possible to have log independent variables in count data models (or, if their coefficients have to be interpreted in a different way).
Thank you for any suggestion!

[Rich Goldstein]

the constant in a -poisson- model (you don't say what command you are using, so...) is the mean of the outcome variable when each predictor is equal to zero (as in linear regression); try the following:

sysuse auto
tab foreign, su(gear)
poisson gear foreign, irr

also, you just said the constant was shown (but basically zero) so why ask why it is not shown - this is very confusing

[Simona Gamba]

Sorry if I was not clear.
I am using a NB model.
In my regression, the constant is shown, and its value in terms of IRR is basically zero.
On the examples I found on the internet (see the links above), they have a model with a constant, but when they show results in terms of IRR they do not show the constant any more. So I was wondering why they did not show the IRR for the constant. However, from your answer, I understand that, independently from what they are doing in the examples I linked, there is nothing wrong in reporting the IRR for the constant.
Thank's

[Svend Juul]

Please tell us: "I am using the nbreg command" if that is the case, rather than the unspecific "a NB model".

In Stata 13, _cons is always displayed, also with the irr option. In prior versions, you can, after nbreg (or poisson or logistic or ...) see it with:

lincom _cons, irr

Hope this helps
Svend

[Richard Williams]

As Rich G. noted, the constant is the expected value when all the explanatory variables equal zero. But, it may not mean much if zero values aren't possible, e.g. Things like weight, height, and age will never equal zero, nor would a scale that is constructed to run from 400 to 1200. So, there is nothing necessarily strange about values like you are getting for the constant; it may basically be the expected value for a case that cannot exist. If you want the constant to be more intuitively meaningful, you can do things like center your variables, I.e. Subtract the mean from each variable. Then the constant becomes the expected value for an "average" person, and a person more or less like that probably does exist. For more about centering, see http://www3.nd.edu/~rwilliam/xsoc63993/l53.pdf

[Richard Williams]

Also, you can have logged independent variables. If the coefficients seem "crazy" it may be because you should scale the variables differently, e. g. Instead of measuring income in pennies you should measure it in thousands or millions of dollars. The scaling won't affect the substantive meaning of the results but it may make the coefficients easier to interpret. That is not to say that logging is a good idea in your case (I have no idea) but you should be aware that so-called "strange" or "crazy" coefficients may just reflect the fact that your variables are scaled or coded in a way that makes interpretation difficult.

[Simona Gamba]

thank you all for your replies, I learned something useful!
Once I rescaled the variables, the value for the constant became definitely more intuitively meaningful.
I just still have some problems in understanding the coefficient for one control variable.
I am regressing (using the nbreg and the zinb commands) the number of patents on some country's characteristics, between which the population.
When I use the level of the population (measured in thousands of individuals) I get an incidence rate ratio of 1.0005. When instead I use the log of the population (in this case, obviously, it doesn't metter if population is measured in thousands or milions), I get an IRR of 13.69091, that means that a 1% increase in the population is associated with an increase in the number of patents of 1269%! Since the average increase in population in my countries is 42%, this corresponds to an increase in the number of patents that seems to me unlikely (and even more unlikely if compared to the results obtained when using the level of the population).
Do you have any idea about why I obtain such discordant results?
Thank you again!

[Jeff Wooldridge]

Simona: You are incorrectly interpreting the irr (which I have never found compelling, anyway). The original coefficient, not the irr, is the elasticity of the count with respect to population. The coefficient must have been roughly 2.6, which is the elasticity. So, a one percent increase in population leads to a 2.6 percent increase in the expected count. I hope this helps. JW

[Jeff Wooldridge]

As a brief follow up -- in the spirit of actually being a teacher of econometrics, rather than a scolder -- the irr allows you to measure the proportionate change when your x increases by one unit. But your x in this case is log(popul), so a one unit increase in x is a percentage increase of 100*exp(1) = 271.82, so a 271.8 percent increase in population. This is clearly not a "marginal" change, and that's why the irr is not useful here. The irr is useful only when a unit increase in x is realistic. For your purposes, the calculation approximation of the coefficient itself seems more useful.

[Simona Gamba]

thank you very much!! you were really clarifing: now I have understood not only how to interprete the coefficients (and which was my mistake) but also why it is like this. I really thank you for the explanation.