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Re: st: nbreg - problem with constant?


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: nbreg - problem with constant?
Date   Fri, 02 Mar 2012 14:11:47 -0500

At 01:34 PM 3/2/2012, Simon Falck wrote:
Hi,

I have some problems in fitting a negative binomial regression model. It seems that one problem is related to the "constant" as the it inflates the coef. If the constant is removed, some coef are still unexpectedly high. Since removing the constant bias coef results implies restrictions, I hope anyone can contribute with some insights on this matter.

I apply the NBREG command to estimate the nr of new firms per country explained by country-characteristics. The dataset is consisted of information for 72 countries over 8 years, N=id=576. The information is annual, all regressors are lagged 1 year (t-1). The dv (Y) is the nr of new firms per country and vary between 0-204. The indepv (X1-X5) are country-specific attributes. Each indepv are continuous and vary across countries (id). No interaction terms are used. Some correlation exist, in general <0.3, but up to 0.6. The dataset is structured as,

id year Y X1 X2 X3 X4 X5 1 2000 10 0.5258504 1.148275 1.623761 0.00905698 0.2926497 2 2000 1 1.105136 0.9730458 0.7427208 0.03010507 0.1732135 3 2000 2 1.342283 0.7757816 0.6444564 0.01280751 0.2596922
...
The model is estimated with command: nbreg Y X1 X2 X3 X4 X5
Generates results:
-----------------
Negative binomial regression                    Number of obs   =       576
LR chi2(8) = 387.39
Dispersion     = mean                           Prob > chi2     =       0.0000
Log likelihood = -562.09431                     Pseudo R2       =       0.2563

Y Coef. Std. Err. z P>z [95% Conf. Interval] X1 .3927241 .3024751 1.30 0.194 -.2001162 .9855644 X2 .6401666 .4818861 1.33 0.184 -.3043129 1.584646 X3 1.27199 .4352673 2.92 0.003 .4188815 2.125098 X4 -5.603575 1.724484 -3.25 0.001 -8.983502 -2.223648 X5 -1.370085 .1557769 -8.80 0.000 -1.675402 -1.064768 Constant 10.5169 2.30579 4.56 0.000 5.997634 15.03617 /lnalpha -.2836582 .1966372 -.66906 .1017437 alpha .753024 .1480725 .5121898 1.1071 Likelihood-ratio test of alpha=0: chibar2(01) = 214.48 Prob>=chibar2 = 0.000
-----------------
The LR-test indicates that Negbin- is preferred over Possion. X1-X2 are insignf., while X3-X5 are signf., P<0.05. We can see that the constant is very large, coef= exp(10.5169)=33225.488 and std.err for X4 is quite high (1.72..).

Without knowing more about the variables, I would be hesitant to say the constant is "large" or the standard error is "quite high." If you, say, rescaled the Xs, or centered each X about its mean, the constant would change. Likewise if you rescaled X4 (e.g. changed it from income in dollars to income in thousands of dollars) the coefficient and standard error for X4 would change. You can think of the constant as being the score a case would have if every X equaled 0, but there may be no such cases where that would ever happen, e.g. in a sample of adults nobody will have a value of 0 years.

In short, it isn't clear to me that you have a problem. If you find the coefficients non-intuitive, then rescaling the Xs in some way or centering them may help.

As a sidelight, your analysis seems to be ignoring your panel structure. You may wish to take a look at the XT manual and/or Paul Allison's book on "Fixed effects regression models."


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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EMAIL:  Richard.A.Williams.5@ND.Edu
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