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

Detailed
Outline

I. Overview(page 466)

A. Focus: modeling outcomes with more than two

levels.

B. Ordinal outcome variables.

II. Ordinal logistic regression: The proportional

odds model(pages 466–472)

A. Ordinal outcome: variable categories have a

natural order.

B. Proportional odds assumption: the odds ratio is

invariant to where the outcome categories are

dichotomized.

C. The form for the proportional odds model with

one independent variable (X 1 ) for an outcome

(D) withGlevels (D¼0, 1, 2,...,G1) is

PðDgjX 1 Þ¼

1

1 þexp½ðagþb 1 X 1 ފ

;

whereg¼ 1 ; 2 ;...;G 1

III. Odds ratios and confidence limits(pages 472–475)

A. Computation of the OR in ordinal regression is

analogous to standard logistic regression,

except that there is a single odds ratio for all

comparisons.

B. The general formula for the odds ratio for

any two levels of the predictor variable

(X** 1 andX* 1 )is

OR¼exp½b 1 ðX 1 **X 1 *ފ

for a model with one independent variable (X 1 ).

C. Confidence interval estimation is analogous to

standard logistic regression.

D. The general large-sample formula for a 95%

confidence interval for any two levels of the

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

exp^b 1 ðX 1 **X 1 *Þ   1 : 96 ðX** 1 X* 1 Þs^b 1

hi

E. The likelihood ratio test is used to test

hypotheses about the significance of the

predictor variable(s).

i. There is one estimated coefficient for each

predictor.

ii. The null hypothesis is that the beta

coefficient (for a given predictor) is equal to

zero.

iii. The test compares the log likelihood of the

full model with the predictor(s) to that of

the reduced model without the predictor(s).

482 13. Ordinal Logistic Regression