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sandwich variance estimation using glmer?

Let me push on this just a bit to spark further discussion. The OP was interested in robust standard errors given misspecification in the likelihood. So, one possible avenue was to explore Huber-White standard errors, or the sandwich estimator, to account for this misspecification and obtain "better" standard errors, but still use the point estimates of the fixed effects as given.

Some discussion on this has noted that the misspecification occurs in many ways, sometimes given that distributional assumptions were not met. Let's assume someone was willing and skilled to code up the HW as a possible solution within lmer to account for not meeting certain distributional assumptions.

My question is now why not directly code up models that permit for different distributional assumptions, such as t-distributions of residuals (random effects) or whatever the case might be? In other words, why not write code that addresses the problems directly (misspecification of the likelihood) rather than focusing on HW estimates.

Isn't it a better use of time and energy to focus on properly specifying the likelihood and estimating parameters from that model rather than HW?