The General Estimating Equation (GEE) is a powerful statistical technique used for analyzing correlated data, particularly longitudinal data or clustered data. It’s a semi-parametric approach that doesn’t require specifying the full joint distribution of the repeated measurements. Instead, GEE focuses on modeling the marginal mean of the outcome variable, accounting for within-subject correlation through a specified working correlation structure. Implementing GEE in R is relatively straightforward using packages like `geepack`.
So, how do you actually perform GEE in R? Here’s a breakdown of the process, along with the core elements needed for implementation. Remember to install and load the `geepack` package first:
install.packages("geepack")
library(geepack)
Now, let’s get to the main answer:
- The `geeglm()` function: This is the primary function within the `geepack` package for fitting GEE models. It’s analogous to `glm()` but specifically designed for correlated data.
- Formula Specification: Just like in `glm()`, you define the relationship between the outcome variable and predictor variables using a formula (e.g., `outcome ~ predictor1 + predictor2`).
- `id` Argument: Crucially, you must specify an `id` variable that identifies the clusters or subjects. This tells the `geeglm()` function which observations belong to the same individual or group, allowing it to account for correlation.
- `family` Argument: This specifies the marginal distribution of the outcome variable, similar to `glm()`. Common options include `gaussian` (for continuous outcomes), `binomial` (for binary outcomes), and `poisson` (for count outcomes).
- `corstr` Argument: This defines the working correlation structure, which approximates the correlation among observations within each cluster. Common options include:
- `”independence”`: Assumes no correlation.
- `”exchangeable”`: Assumes a constant correlation between any two observations within a cluster.
- `”ar1″`: Assumes an autoregressive order 1 correlation structure.
- `”unstructured”`: Estimates a separate correlation for each pair of observations within a cluster (requires sufficient data per cluster).
- Example:
geeglm(outcome ~ predictor1 + predictor2, id = subject_id, family = gaussian, data = mydata, corstr = "exchangeable")
Remember to carefully consider the choice of working correlation structure, as it can impact the efficiency of the estimators. While GEE is robust to misspecification of the correlation structure (in terms of consistent estimation of the regression coefficients), choosing a more appropriate structure can lead to more precise estimates.
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