I understand that both methods can be utilized to obtain correct inference in overdispersed Poisson data. What I don't understand is the difference between them: why the analyst would choose one over the other, how they are estimated, and how it affects inference.

I have read the vignette countreg in (http://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf), so I have seen theorical distinctions, but I do not know how and why to select between these two types of covariance estimators in practice.


1 Answer 1


From a purely applied perspective, my experience is that the difference between these methods is typically not huge, leading to qualitatively the same conclusions (see Table 2 in the vignette you referenced). Therefore, choosing one or the other in practice is often more a matter of taste than due to the actual properties. In the classic parametric statistics literature the quasi-Poisson model is well known due to coverage in the classical "Generalized Linear Models" book by McCullagh & Nelder. However, in econometrics, social or political science, so-called "robust" sandwich standard errors are very common and hence also often used in the presence of (potential) overdispersion.

From a more theoretical perspective, the sandwich approach has the property to guard against more potential departures from the Poisson model while the quasi-Poisson is geared directly towards overdispersion. Hence, the quasi-Poisson (as well as the negative binomial) model just requires estimation of a single additional parameter. In contrast, the sandwich covariance matrix implicitly allows for a different variances for each observation and thus needs to estimate more in a certain sense.

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    $\begingroup$ If the answer was useful for you please accept it here on StackExchange so that the question is flagged as "answered". $\endgroup$ Commented Oct 8, 2017 at 9:15
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    $\begingroup$ By the "sandwich covariance matrix" needing to estimate more, I might clarify the implication is that sandwich covariance is more general, yet slightly inefficient compared to quasipoisson when the stronger assumptions are met. That is to say, if you know the variance is merely proportional to the mean (with the dispersion being the proportionality constant), quasipoisson is the better choice. $\endgroup$
    – AdamO
    Commented Mar 9, 2018 at 16:37

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