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From a slides

How does GEE work?

  • First, a naive linear regression analysis is carried out, assuming the observations within subjects are independent.
  • Then, residuals are calculated from the naive model (observed-predicted) and a working correlation matrix is estimated from these residuals.
  • Then the regression coefficients are refit, correcting for the correlation. (Iterative process)
  • The within-subject correlation structure is treated as a nuisance variable (i.e. as a covariate)

I was wondering in step 2, how is the working correlation matrix estimated for GEE?

What is "the naive model"?

Thanks!

Tim
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1 Answers1

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If you look at the note (and your quotation) specifically, "The data in long form could be naively thrown into an ordinary least squares (OLS) linear regression…ignoring the correlation between subjects."

A good reference for your question is Liang and Zeger (1986) on Biometrika. Section 3.3 shows that the correlation parameters $\alpha$ can be estimated from the Pearson residuals $\hat{r}_{it}$. The specific estimator depends on the choice of working correlation matrix $R(\alpha)$ (independent, exchangeable, autoregressive, M-dependent or unstructured). The general approach is $$\hat{R}_{uv}=\Sigma_{i=1}^K\hat{r}_{iu}\hat{r}_{iv}/(N-p).$$ Specific estimators are given in section 4.

Randel
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