Hello, I am running a negative binomial model using the glm.nb function in MASS
package. But the standard errors I get are slightly different from the same
model I ran using Stata's nbreg command. Some of the standard errors are the
same, but some are not. Those that are different differ in their decimals,
particularly the third decimal. I am wondering how exactly glm.nb calculates
standard errors. I could not find any documentation. The standard errors in
Stata's nbreg command are calculated from the observed information matrix. I am
thinking that maybe glm.nb uses the expected information instead of the
observed information? But I could not figure out if that is the case. It may be
because I don't have a very good grasp of the difference between expected and
observed information. I also tried to look into the source code of glm.nb by
typing glm.nb in the R console, but I could not find how the standard errors
are calculated. Any help will be very much appreciated! As a side note, here is
the output I get after running the glm.nb model: Deviance Residuals: Min
1Q Median 3Q Max -2.8076 -1.0216 -0.4800 0.3257
4.2359 Coefficients: Estimate Std. Error
z value Pr(>|z|) (Intercept) -1.4211390 0.2334931
-6.086 1.15e-09 *** x1 -0.0633597 0.1825984
-0.347 0.728599 x2 0.0240531 0.0327962
0.733 0.463308 x3 -0.0223691 0.0318900
-0.701 0.483025 x4 0.1004497 0.0348040
2.886 0.003900 ** x5 -0.0110895 0.0254989
-0.435 0.663635 x6 0.0098525 0.0174814
0.564 0.573029 x7 -0.2574358 0.2375014
-1.084 0.278394 x8 0.0319359 0.0250482
1.275 0.202318 x9 0.9795687 0.0332084
29.498 < 2e-16 *** x10 -1.2697342 0.1684822
-7.536 4.83e-14 *** x11 0.0021235 0.0003019
7.035 2.00e-12 *** x12 0.5223974 0.2052481 2.545
0.010922 * x13 -0.0491496 0.1853978 -0.265
0.790930 x14 -0.4071932 0.1087920 -3.743
0.000182 *** x15 -0.2980707 0.2197779 -1.356
0.175024 x16 -0.2374620 0.1885971 -1.259
0.207995 x17 -0.1466253 0.1236171 -1.186
0.235573 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for Negative Binomial(1.2214) family taken to be 1)
Null deviance: 3658.9 on 1108 degrees of freedom Residual deviance: 1186.1
on 1091 degrees of freedom (34 observations deleted due to missingness) AIC:
5104.4 Number of Fisher Scoring iterations: 1 Theta: 1.2214
Std. Err.: 0.0855 2 x log-likelihood: -5066.3860
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