[R-meta] sandwhich estimator with geeglm object

[James Pustejovsky]

Hi Yefeng,

Yes, this is correct if we're speaking on a very broad level. Broadly,
geepack::geeglm() with an identity link function fits the same type of
model as nlme::gls(), but geepack::geeglm() uses sandwich variance
estimation whereas nlme::gls() uses model-based variance estimation.
Running nlme::gls() with clubSandwich::vcovCR() will give you sandwich
variance estimation. The CR1 and CR3 sandwich estimators can be calculated
from both packages for comparison purposes.

There is one other difference that should be noted though:
geepack::geeglm() uses moment estimators for the parameters of the working
model (such as variance coefficients, auto-correlation terms, etc.). In
contrast, nlme::gls() uses maximum likelihood or restricted maximum
likelihood estimation for these parameters. This difference in estimation
strategies can lead to numerical differences in the model coefficient
estimates calculated by the two packages  (and therefore also differences
in the sandwich standard errors generated by geepack::geeglm versus by
clubSandwich::vcovCR.gls).

James

On Mon, May 1, 2023 at 7:19 PM Yefeng Yang <yefeng.yang1 using unsw.edu.au> wrote:

> Dear James,
> Probably, it is more clear if I ask "whether glm + RVE is equal to gee?".
> gee is doing RVE on the fly, while glm + RVE uses a post-hoc way to
> calculate robust errors when dealing with correlated errors (e.g., repeated
> measurements).
> Best,
> Yefeng
>
> ------------------------------
> *From:* James Pustejovsky <jepusto using gmail.com>
> *Sent:* Tuesday, 2 May 2023 0:55
> *To:* R Special Interest Group for Meta-Analysis <
> r-sig-meta-analysis using r-project.org>
> *Cc:* Yefeng Yang <yefeng.yang1 using unsw.edu.au>
> *Subject:* Re: [R-meta] sandwhich estimator with geeglm object
>
> Hi Yefeng,
>
> geeglm is currently available in the development version of clubSandwich.
> We are including support for GEE models because clubSandwich implements
> small-sample corrections to the sandwich variance estimator and to the
> degrees of freedom, which are not available in geepack. McCaffrey and Bell
> (2006; https://doi.org/10.1002/sim.2502) showed that these small-sample
> corrections perform better than the standard sandwich estimators and
> large-sample test statistics implemented in geepack.
>
> GEE is not equivalent to GLS. Rather, geepack::geeglm() is to glm() as
> nlme::gls() is to lm(). GEE models allow non-linear link functions for the
> conditional expectation of the outcome. Of course, gls is a special case of
> geeglm with an identity link function (just as lm is a special case of
> glm).
>
> James
>
> On Mon, May 1, 2023 at 4:15 AM Yefeng Yang via R-sig-meta-analysis <
> r-sig-meta-analysis using r-project.org> wrote:
>
> Dear experts,
>
> I would be grateful if anyone can address my confusion concerning robust
> variance estimation (especially via the implementation of clubsandwich
> package).
>
> First question:
> geeglm object refers to the regression model fitted by Generalized
> Estimating Equations (GEE), which can be implemented in package geepack.
> Given that GEE already calculates cluster robust errors to account for
> mids-specified var-cov structure (e.g., autocorrelation), why clubsandwich
> still calculate robust errors for geeglm object
>
> Second question:
> GEE basically relaxes the assumption about var-cov structure and it uses a
> working var-cov structure (usually misspecified) to get beta coefficient
> and then uses the sandwich estimator to estimate sampling variances
> Var(beta) or standard error SE(beta). In this sense, GEE is equivalent to
> generalized least squares (say fitted by gls()) with CRVE. Am I correct?
>
>
> Best,
> Yefeng
>
>
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>
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