STAT 541: Generalized Estimating Equations

# Statistics 541: Generalized Estimating Equations

• My grandmother (who is 99) is in the hospital--so I might miss some days. I'll try to send in a replacement.

## Generalized Estimating Equations

General problem: Observe the same person over time. Say in medicine, you might follow the effect of a drug. I education you might follow the effect of various teaching styles, or interactive learning methods. In business you might follow the course of various incentive plans for sales people.

Assumption: each person is independent of all other people, but depends highly on themselves.

Model:

Y = X beta + noise

But the noise is NOT independent. But the dependence is not easilly modelled. Alternatively, you might not believe the model even if it were easy to come up with.

Model notation:

• jij ith person jth observation
• i = 1..K
• j = 1..ni (or more easilly j = 1..n)
• E.g. blood pressure measurement at 3 visits to doctor
• There are X's also! Need 3 indexes--but lets use vectors
• xij = vector of ith person jth observation covariates
• see eqn for density and mean and variance
• E(y) = a'(theta), var(y) = a''(theta)/phi
Random effects example:
• corr(yit,yit') = alpha
• Eg yit = E(y) + epsiloni + epsilonit
• covariance is capture in epsiloni
• (example 3 in paper)
Time series example:
• corr(yit,yit') = alpha|t-t'|
• eg: yit = AR(1) process (aka an OU process)
• (example 4 in paper)