268 PART 5 Looking for Relationships with Correlation and Regression

While it is relatively easy to identify if there is a perfect predictor in your data set

by looking at frequencies, you may run into the perfect predictor problem as a

result of a combination of predictors in your model. Unfortunately, there aren’t

any great solutions to this problem. One proposed solution called the Firth correc-

tion allows you to add a small number roughly equivalent to half an observation

to the data set that will disrupt the complete separation. If you can do this correc-

tion in your software, it will produce output, but the results will likely be unstable

(very near 0, or very near infinity). The approach of trying to fix the model by

changing the predictors would not make sense, since the model fits perfectly. You

may be forced to abandon your logistic regression plans and instead provide a

descriptive analysis.

Figuring Out the Sample Size You

Need for Logistic Regression

Estimating the required sample size for a logistic regression can be a pain, even

for a simple one-predictor model. You will have no problem specifying desired

power and α level (see Chapter 3 for more about these items). And, you can state

the effect size of importance as an OR.

FIGURE 18-8:

Visualizing the

complete

separation (or

perfect predictor)

problem in

logistic

regression.

© John Wiley & Sons, Inc.