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

i. A mean–variance relationship for the

responses is specified.

ii. The full likelihood is not specified.

VI. GEE models(pages 506–507)

A. GEE are generalizations of GLM.

B. In GEE models, as in GLM, a link function [g(m)]

is modeled as linear in the regression parameters.

i. The logit link function is commonly used for

dichotomous outcomes:

gðmÞ¼logit½PðD¼ 1 jXފ¼b 0 þ~

p

h¼ 1

bhXh

ii. This model form is identical to the standard

logistic model, but the underlying

assumptions differ.

C. To apply a GEE model, a “working” correlation

structure for within-cluster correlations is

specified.

VII. Correlation structure(pages 507 – 510)

A. A correlation matrix in which responses are

correlated within subjects and independent

between subjects is in the form of ablock

diagonal matrix.

i. Subject-specific matrices make up blocks

along the diagonal.

ii. All nondiagonal block entries are zero.

B. In a GEE model, each subject (cluster) has a

common set of correlation parameters.

VIII. Different types of correlation structures
(pages 511–516)
A. Independentcorrelation structure
i. Assumption: responses within a cluster are
uncorrelated.
ii. The matrix for a given cluster is the identity
matrix.
B. Exchangeablecorrelation structure
i. Assumption: any two responses within a
cluster have the same correlation (r).
ii. Only one correlation parameter is
estimated.
iii. Therefore, the order of observations within
a cluster is arbitrary.
C. Autoregressivecorrelation structure
i. Often appropriate when there are repeated
responses over time.

Detailed Outline 531