# [R] How are the standard errors of the estimates in glm.nb() calculated?

정재희 jenn1120 at naver.com
Tue Nov 11 18:58:44 CET 2014

```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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