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

Discriminant function analysis:

 Previously used for logistic
model

 Restrictive normality
assumptions

 Gives biased results – odds
ratio too high

ML estimation:

 No restrictions on independent
variables

 Preferred to discriminant
analysis

III. Unconditional vs.
Conditional Methods

Two alternative ML approaches:

1. Unconditional method


2. Conditional method

 Require different computer
algorithms

 User must choose appropriate
algorithm

Computer Programs

SAS
SPSS
Stata

Until the availability of computer software for

ML estimation, the method used to estimate

the parameters of a logistic model wasdiscrim-

inant function analysis. This method has been

shown by statisticians to be essentially a

least squares approach. Restrictive normality

assumptions on the independent variables in

the model are required to make statistical

inferences about the model parameters. In par-

ticular, if any of the independent variables are

dichotomous or categorical in nature, then the

discriminant function method tends to give

biased results, usually giving estimated odds

ratios that are too high.

ML estimation, on the other hand, requires no

restrictions of any kind on the characteristics

of the independent variables. Thus, when using

ML estimation, the independent variables can

be nominal, ordinal, and/or interval. Conse-

quently, ML estimation is to be preferred over

discriminant function analysis for fitting the

logistic model.

There are actually two alternative ML

approaches that can be used to estimate the

parameters in a logistic model. These are called

theunconditional methodand theconditional

method. These two methods require different

computer algorithms. Thus, researchers using

logistic regression modeling must decide

which of these two algorithms is appropriate

for their data. (See Computer Appendix.)

Three of the most widely available computer

packages for unconditional ML estimation of

the logistic model are SAS, SPSS, and Stata.

Programs for conditional ML estimation are

available in all three packages, but some are

restricted to special cases. (See Computer

Appendix.)

Presentation: III. Unconditional vs. Conditional Methods 107