Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

To test several^bh simultaneously
use

 Score test

 Generalized Wald test

UnderH 0 , test statistics approxi-
matew^2 with df¼number of para-
meters tested.

To test one^bh, the Wald test statis-
tic is of the familiar form

Z¼

^bh

s^bh

Next two sections:

 GEE theory

 Use calculus and matrix
notation

The Score test, as with the likelihood ratio test,

can be used to test several parameter estimates

simultaneously (i.e., used as a chunk test).

There is also a generalized Wald test that can

be used to test several parameter estimates

simultaneously.

The test statistics for both the Score test

and the generalized Wald test are similar to

the likelihood ratio test in that they follow an

approximate chi-square distribution under the

null with the degrees of freedom equal to the

number of parameters that are tested. When

testing a single parameter, the generalized

Wald test statistic reduces to the familiar

form ^bh divided by the estimated standard

error ofb^h.

The use of the Score test, Wald test, and

generalized Wald test will be further illustrated

in the examples presented in the Chap. 15.

In the final two sections of this chapter we dis-

cuss the estimating equations used for GLM

and GEE models. It is the estimating equations

that form the underpinnings of a GEE analysis.

The formulas presented use calculus and

matrix notation for simplification. Although

helpful, a background in these mathematical

disciplines is not essential for an understanding

of the material.

520 14. Logistic Regression for Correlated Data: GEE