STAT 541: Generalized Estimating Equations

# Statistics 541: Generalized Estimating Equations

## Admistrivia

- 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:

- j
_{ij} ith person jth observation
- i = 1..K
- j = 1..n
_{i} (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
- x
_{ij} = 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(y
_{it},y_{it'}) = alpha
- Eg y
_{it} = E(y) + epsilon_{i} + epsilon_{it}
- covariance is capture in epsilon
_{i}
- (example 3 in paper)

Time series example:
- corr(y
_{it},y_{it'}) = alpha^{|t-t'|}
- eg: y
_{it} = AR(1) process (aka an OU process)
- (example 4 in paper)

*
*
Last modified: Tue Apr 10 08:21:43 2001

*
*