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

Detailed
Outline I. Overview(pages 432–433)
A. Focus: modeling outcomes with more than two
levels.
B. Using previously described techniques by
combining outcome categories.
C. Nominal vs. ordinal outcomes.
II. Polytomous logistic regression: An example with
three categories(pages 434–437)
A. Nominal outcome: variable has no inherent
order.
B. Consider “odds-like” expressions, which are
ratios of probabilities.
C. Example with three categories and one
predictor (X 1 ):

ln

PðD¼ 1 jX 1 Þ

PðD¼ 0 jX 1 Þ



¼a 1 þb 11 X 1 ;

ln

PðD¼ 2 jX 1 Þ

PðD¼ 0 jX 1 Þ



¼a 2 þb 21 X 1 :

III. Odds ratio with three categories(pages 437–441)

A. Computation of OR in polytomous regression is

analogous to standard logistic regression, except

that there is a separate odds ratio for each

comparison.

B. The general formula for the odds ratio for any

two levels of the exposure variable (X** 1 andX* 1 )in

a no-interaction model is

ORg¼expðbg 1 X** 1 X* 1

hi

; whereg¼ 1 ; 2 :

IV. Statistical inference with three categories

(pages 441–444)

A. Two types of statistical inferences are often of

interest in polytomous regression:

i. Testing hypotheses

ii. Deriving interval estimates

B. Confidence interval estimation is analogous to

standard logistic regression.

C. The general large-sample formula (no-

interaction model) for a 95% confidence interval

for comparison of outcome levelgvs. the

reference category, for any two levels of the

independent variable (X 1 **andX 1 *), is

exp ^bg 1 X** 1 X* 1



 1 : 96 X* 1 X 1



s^bg 1

no

:

Detailed Outline 455