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

B. Correlation: a standardized measure of

covariance that is scale-free.

rxy¼

covðX;YÞ

sXsY

i. Correlation values range from1toþ1.

ii. Can have correlations between

observations on the same outcome variable.

iii. Can have correlations between

dichotomous variables.

C. Correlation between observations in a cluster

should be accounted for in the analysis.

V. Generalized linear models(pages 503 – 506)

A. Models in the class of GLM include logistic

regression, linear regression, and Poisson

regression.

B. Generalized linear model withppredictors is of

the form

gðmÞ¼b 0 þ~

p

i¼ 1

biXi;

wheremis the mean response andg(m)isa

function of the mean

C. Three criteria for a GLM:

i. Random component: the outcome follows a

distribution from the exponential family.

ii. Systematic component: the regression

parameters are modeled linearly, as a

function of the mean.

iii. Link function [g(m)]: this is the function

that is modeled linearly with respect to the

regression parameters:

a. Link function for logistic regression:

logit function.

b. Inverse of link function [g^1 (X,b)]¼m.

c. For logistic regression, the inverse of the

logit function is the familiar logistic

model for the probability of an event:

g^1 ðX;bÞ¼m¼

1

1 þexp aþ~

p

i¼ 1

biXi



D. GLM uses maximum likelihood methods for

parameter estimation, which require

specification of the full likelihood.

E. Quasi-likelihood methods provide an

alternative approach to model development.

530 14. Logistic Regression for Correlated Data: GEE