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

ii. Empirical (robust) estimators, which are an

adjustment of model-based estimators:

a. Make use of the actual correlations

between responses in the data as well as

the specified correlation structure.

b. Are consistent even if the correlation

structure is misspecified.

X. Statistical tests(pages 519 – 520)

A. Score test

i. The test statistic is based on the “score-like”

equations.

ii. Under the null, the test statistic is

distributed approximately chi-square with

df equal to the number of parameters

tested.

B. Wald test

i. For testing one parameter, the Wald test

statistic is of the familiar form

Z¼

b^

s^b

:

ii. For testing more than one parameter, the

generalized Wald testcan be used.

iii. The generalized Wald test statistic is

distributed approximately chi-square with

df equal to the number of parameters

approximate tested.

C. In GEE, the likelihood ratio test cannot be used

because the likelihood is never formulated.

XI. Score equations and “score-like” equations
(pages 521 – 523)
A. For maximum likelihood estimation,score
equationsare formulated by setting the partial
derivatives of the log likelihood to zero for each
unknown parameter.
B. In GLM, score equations can be expressed in
terms of the means and variances of the
responses.
i. Givenpþ1 beta parameters andbhas the
(hþ1)st parameter, the (hþ1)st score
equation is

~

K

i¼ 1

@mi

bh

½varðYiފ^1 ½YimiŠ¼ 0 ;

whereh¼0, 1, 2,...,p.

ii. Note there arepþ1 score equations, with

summation over allKsubjects.

Detailed Outline 533