### XLISP-Stat estimates Generalised Estimating Equations

XLISP-Stat tools for building Generalised Estimating Equation models

offers an introduction to GEE models.

Much of the brain trust of XLISP Stat has moved on to r.

Generalised Estimating Equations models, proposed by Liang and Zeger

in 1986, are probably the simplest method for analysing data collected

in groups where observations within a group may be correlated but

observations in separate groups are independent. A complete

description of the method is given in their two 1986 papers. The basic

principle of the method is a generalisation of the fact that weighted

least squares analyses give unbiased parameter estimates no matter

what weights are used. Generalised linear models, such as logistic

regression, have similar robustness properties, giving asymptotically

correct parameter estimates even when the data are correlated. This

means that it is possible to estimate regression parameters using any

convenient or plausible assumptions about the true correlation between

observations and get the right answer even when the assumptions are

not correct.

It is only necessary to use a ``model-robust'' or ``agnostic''

estimate of the standard errors. It would be unreasonable to expect

this freedom of choice to be without cost and it turns out that there

is a moderate gain in efficiency resulting from choosing a working

correlation structure close to the true one.

Useful references include the two original papers (Zeger & Liang 1986,

Liang & Zeger 1986) and two recent books: Diggle, Liang & Zeger (1993)

and Fahrmeir & Tutz (1995). As far as I know the most elementary

treatment anywhere in the literature is still Zeger & Liang (1986).

Section 2 gives an overview of the theory and use of Generalised

Estimating Equations. Section 3 describes how to use the Lisp-Stat

code, including diagnostics. Finally there is a brief discussion of

missing data handling and of other software for fitting GEE models.

Appendix A describes some aspects of the implementation, including the

global variables (Table 5) that control many program options.