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

VII. Polytomous vs.

Multiple Standard

Logistic Regressions

Polytomous vs. separate logistic

models

Polytomous model uses data on all

outcome categories inL.

Separate standard logistic model

uses data ononly two outcome

categories at a time:

+

Parameter and variance estimates

may differ:

Special case: One dichotomous

predictor Polytomous and stan-

dard logistic models ) same

estimates

One may wonder how using a polytomous

model compares with using two or more sepa-

rate dichotomous logistic models.

The likelihood function for the polytomous

model utilizes the data involving all categories

of the outcome variable in a single structure. In

contrast, the likelihood function for a dichoto-

mous logistic model utilizes the data involving

only two categories of the outcome variable. In

other words, different likelihood functions are

used when fitting each dichotomous model

separately than when fitting a polytomous

model that considers all levels simultaneously.

Consequently, both the estimation of the para-

meters and the estimation of the variances

of the parameter estimates may differ when

comparing the results from fitting separate

dichotomous models to the results from the

polytomous model.

In the special case of a polytomous model with

one dichotomous predictor, fitting separate

logistic models yields the same parameter esti-

mates and variance estimates as fitting the

polytomous model.

We suggest that you review the material cov-

ered here by reading the detailed outline that

follows. Then, do the practice exercises and

test.

VIII. SUMMARY

3 Chapter 9: Polytomous Logistic
Regression

This presentation is now complete. We have

described a method of analysis, polytomous

regression, for the situation where the out-

come variable has more than two categories.

Presentation: VIII. Summary 453