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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?

EJ16
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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.

Michael R. Chernick
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    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. – EJ16 Apr 13 '17 at 01:40
  • 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. – Michael R. Chernick Apr 13 '17 at 01:44
  • 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? – EJ16 Apr 13 '17 at 01:53
  • 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. – Michael R. Chernick Apr 13 '17 at 01:58
  • GEE is a quasi-likelihood model. It relaxes the assumptions of the joint distributions so MLE is not required. GEE is especially popular with repeated observations. I'm assuming this is how it also associated with the nuisance, since with MLE you pick good parameters with it. So, it's finally starting to make some sense now given the focus on parameters like you said. But they say that with GEE the w/in subject correlation is treated as a nuisance variable. I guess that's the part I'm not totally getting. – EJ16 Apr 13 '17 at 02:30
  • @MonicaW. So is my answer starting to look good to you? I know about GEE (at least I used to). The within subject correlation is a distribution parameter. An estimate of it is a variable. I guess it is not the within subject correlation that is the objective of the analysis. Hence it can be a nuisance parameter. – Michael R. Chernick Apr 13 '17 at 02:50
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    @Michael Since you know about GEE, why not illustrate your answer with a simple GEE situation? – whuber Apr 13 '17 at 14:17