[R-meta] sandwhich estimator with geeglm object

[Yefeng Yang]

Dear James,
Thanks for your clarity. Sorry that my second question is not that clear. I know GEE can accommodate error distributions other than Gaussian distribution. The situation I want to ask is the normal error distribution (or identity link function). I want to confirm that normal error distribution, whether GEE (fitted by geepack::geeglm() is theoretically equivalent to GLS + sandwich estimator (fitted by nlme::gls() + clubsandwhich). We assume both cases use the naive robust error. Because your answer "gls is a special case of geeglm with an identity link function" does not mention gls + sandwich estimator, so I want to confirm. Very much appreciate your time to address my confusion.

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<mailto: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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