In my trying to further unpack generalized estimating equations, I keep coming across these terms. But after a whirlwind of searching on Google, I really have no idea what it is. What does it mean when the covariance structures are treated as a nuisance, and to only model the mean response? I understand the model is merely estimating, there are weak assumptions with the joint distribution, and there is no maximum likelihood. But I am having a hard time with the terminology. In a similar light, what are nuisance parameters? If nuisance variables are defined as being of no particular interest, why does GEE assume variables to be nuisance?
1 Answer
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Take this case as a illustrative example. Suppose you are trying to estimate the mean of a normal distribution. The normal distribution has a mean and a variance. The variance is a nuisance parameter when estimating the mean. In this case the nuisance parameter can be eliminated because you can create a pivotal quantity that doesn't depend on the variance because you can use the sample variance to form a t distribution which is a function of the degrees of freedom alone.
answered Apr 13, 2017 at 1:33
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1$\begingroup$ Michael, thank you. But I'm not entire sure why I can't wrap my head around this one. You lost me at the t-distribution. $\endgroup$– EJ16Commented Apr 13, 2017 at 1:40
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1$\begingroup$ The t distribution doesn't depend on the nuisance parameter. So in this specific case we can estimate the mean and compute confidence intervals for the mean. I picked this example because the population variance is the nuisance parameter. $\endgroup$ Commented Apr 13, 2017 at 1:44
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$\begingroup$ I read one definition of a nuisance variable of being one that is related to the dependent variable but is of no experimental interest. How does GEE assume the variables to all be nuisance? I'm just not getting it for some reason. Because it's just estimating the means? $\endgroup$– EJ16Commented Apr 13, 2017 at 1:53
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$\begingroup$ I think you should consider it a parameter rather than a variable. When the goal is to estimate the mean, the variance is of no interest but is an obstacle to achieve the goal. So you are correct. I do not know what the case is with generalized estimating equations. $\endgroup$ Commented Apr 13, 2017 at 1:58
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2$\begingroup$ @Michael Since you know about GEE, why not illustrate your answer with a simple GEE situation? $\endgroup$– whuber ♦Commented Apr 13, 2017 at 14:17