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

C. Quasi-likelihood estimating equations follow

the same form as score equations and thus are

called “score-like”equations.

i. For quasi-likelihood methods, a mean

variance relationship for the responses is

specified [V(m)] but the likelihood in not

formulated.

ii. For a dichotomous outcome with a

binomial distribution, var(Y)¼fV(m),

whereV(m)¼m(1m) andf¼1; in general

fis a scale factor that allows for extra

variability inY.

XII. Generalizing the “score-like” equations to form

GEE models(pages 524 – 528)

A. GEE can be used to model clustered data that

contains within cluster correlation.

B. Matrix notation is used to describe GEE:

i. Di¼diagonal matrix, with variance

functionV(mij) on diagonal.

ii. Ci¼correlation matrix (or working

correlation matrix).

iii. Wi¼variance–covariance matrix (or

working covariance matrix).

C. The form of GEE is similar to score equations:

~

K

i¼ 1

@m^0 i

bh

½WiŠ^1 ½YimiŠ¼ 0 ;

whereWi¼fD

(^12)
iCiD
(^12)
iand whereh¼0, 1, 2,...,p.
i. There arepþ1 estimating equations, with
the summation over allKsubjects.
ii. The key difference between generalized
estimating equations and GLM score
equations is that the GEE allow for multiple
responses from each subject.
D. Three types of parameters in a GEE model:
i. Regression parameters (b): these express
the relationship between the predictors and
the outcome. In logistic regression, the
betas allow estimation of odds ratios.
ii. Correlation parameters (a): these express
the within-cluster correlation. A working
correlation structure is specified to run a
GEE model.
iii. Scale factor (f): this accounts for extra
variation (underdispersion or
overdispersion) of the response.
534 14. Logistic Regression for Correlated Data: GEE