sandwich variance estimation using glmer?
One slightly different perspective on robust SE in mixed models: The place where I have seen these used regularly is in the HLM software (popular in education and psychology circles). HLM *always* reports both "standard" and robust SE. What I find interesting is that if you read Raudenbush and Bryk (and the HLM manual), they suggest using the robust SE as a model diagnostic (my term). That is, when there is a discrepancy between SE, they rightly note that something is amiss, and you should do further detective work related to the random-effects specification. That seems like a very valid use of robust SE, though I fully acknowledge such info (ie, model isn't fitting well) could be got other ways. [BTW, I'd love to see other robust approaches, such as t-distributed error and/or priors, but as Ben notes that's an awfully high bar to implement -- either in lmer or MCMCglmm. The heavy package is an initial attempt, but seems to be "stalled out" at the moment.] For what it's worth. cheers, Dave
Harold wrote:
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?
Dave Atkins, PhD Research Associate Professor Department of Psychiatry and Behavioral Science University of Washington datkins at u.washington.edu Center for the Study of Health and Risk Behaviors (CSHRB) 1100 NE 45th Street, Suite 300 Seattle, WA 98105 206-616-3879 http://depts.washington.edu/cshrb/ (Mon-Wed) Center for Healthcare Improvement, for Addictions, Mental Illness, Medically Vulnerable Populations (CHAMMP) 325 9th Avenue, 2HH-15 Box 359911 Seattle, WA 98104 http://www.chammp.org (Thurs)