[R] Comparison of glm.nb and negbin from the package aod

[Matthieu Lesnoff]

Dear Sabine

In negbin(aod), the deviance is calculated by:

# full model
logL.max <- sum(dpois(x = y, lambda = y, log = TRUE))
# fitted model
logL <- -res$value
dev <- -2 * (logL - logL.max)

(the log-Lik contain all the constants)

As Ben Bolker said, whatever the formula used for deviance, differences 
between deviances of two models should be the same

Regards

-- 
------------------
Matthieu Lesnoff

On 10/02/2011 18:00, sabwo wrote:
>
> I have fitted the faults.data to glm.nb and to the function negbin from the
> package aod. The output of both is the following:
>
> summary(glm.nb(n~ll, data=faults))
>
> Call:
> glm.nb(formula = n ~ ll, data = faults, init.theta = 8.667407437,
>      link = log)
>
> Deviance Residuals:
>      Min       1Q   Median       3Q      Max
> -2.0470  -0.7815  -0.1723   0.4275   2.0896
>
> Coefficients:
>              Estimate Std. Error z value Pr(>|z|)
> (Intercept)  -3.7951     1.4577  -2.603  0.00923 **
> ll            0.9378     0.2280   4.114 3.89e-05 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> (Dispersion parameter for Negative Binomial(8.6674) family taken to be 1)
>
>      Null deviance: 50.28  on 31  degrees of freedom
> Residual deviance: 30.67  on 30  degrees of freedom
> AIC: 181.39
>
> Number of Fisher Scoring iterations: 1
>
>
>                Theta:  8.67
>            Std. Err.:  4.17
>
>   2 x log-likelihood:  -175.387
>
> the output of the function negbin with a global dispersion parameter should
> - when i understood it right - yield the same estimates as glm.nb.  it does,
> with slightly little differences.
>
>> negbin(n~ll,~1, data=faults)
> Negative-binomial model
> -----------------------
> negbin(formula = n ~ ll, random = ~1, data = faults)
>
> Convergence was obtained after 112 iterations.
>
> Fixed-effect coefficients:
>                Estimate Std. Error    z value Pr(>  |z|)
> (Intercept) -3.795e+00  1.421e+00 -2.671e+00 7.570e-03
> ll           9.378e-01  2.221e-01  4.222e+00 2.417e-05
>
> Overdispersion coefficients:
>                   Estimate Std. Error   z value   Pr(>  z)
> phi.(Intercept) 1.154e-01   5.56e-02 2.076e+00 1.895e-02
>
> Log-likelihood statistics
>    Log-lik     nbpar   df res.  Deviance       AIC      AICc
> -8.77e+01         3        29 5.209e+01 1.814e+02 1.822e+02
>
> The thing i really dont understand is why there is such a big difference
> between the deviances? (glm.nb = 30.67 and negbin=52.09?) Shouldnt they be
> nearly the same??
>
> thanks for your help,
> sabine