12.4 What Metric Should We Use?
Which link function should we use…does it matter?
- logistic regression using a logit
- probit
- complementary log-log
| logLik | link |
|---|---|
| -380.0873 | logit |
| -381.7535 | probit |
| -389.0645 | c-log-log |
If we just look at the log-likelihood statistic, the logistic link function appears to be statistically (significantly) better than the probit and complementary log-log link functions.
However, if we use the area under the ROC curve, we see that there is no significant difference between the three link functions. When we plot the three link functions, we also see that they are not substantially different in predicting whether a house has central air.
