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

F. The Wald test is analogous to standard logistic

regression.

IV. Extending the ordinal model(pages 476–478)

A. The general form of the proportional odds

model forGoutcome categories andk

independent variables is

PðDgjXÞ¼

1

1 þexp ðagþ~

k

i¼ 1

biXiÞ



B. The calculation of the odds ratio, confidence

intervals, and hypothesis testing using the

likelihood ratio and Wald tests remain the same.

C. Interaction terms can be added and tested in a

manner analogous to standard logistic

regression.

V. Likelihood function for ordinal model(pages

478–479)

A. For an outcome variable withGcategories, the

likelihood function is

Yn

j¼ 1

GY 1

g¼ 0

PðD¼gjXyjgÞ;

where

yjg¼ 1 if the jth subject hasD¼g

0 if otherwise

n

where nis the total number of subjects,g¼

0, 1,...,G1and

P(D¼g|X)¼[P(Dg|X)][P(Dgþ1) |X)].

VI. Ordinal vs. multiple standard logistic regressions
(pages 479–481)
A. Proportional odds model: order of outcome
considered.
B. Alternative: several logistic regressions models
i. One for each cut-point dichotomizing the
outcome categories.
ii. Example: for an outcome with four
categories (0, 1, 2, 3), we have three possible
models.
C. If the proportional odds assumption is met, it
allows the use of one parameter estimate for the
effect of the predictor, rather than separate
estimates from several standard logistic models.

Detailed Outline 483