Interpreting Nagelkerke R2

[epichick]

Hi there,

Can anyone tell me how to interpret the Nagelkerke R2 for logistic
regression? I understand that a Nagelkerke R2 of .78 would mean that
the model accounts for 78% of the variability in the dependent
variable, but what does that really mean? Does it mean that 78% of the
sample would experience the condition (dependent variable=1), if the
independent variables were present? Thanks....

[SR Millis]

Unfortunately, there's not an intuitive interpretation for the various pseudo-R^2s that can be derived in logistic regression. Quite literally, these R^2s represent the proportional reduction in the absolute value of the log-likelihood measure---not the amount of variance accounted for, as in the OLS context.

 

When evaluation logistic regression models, it is much better to focus on model calibration (via Hosmer-Lemeshow GOF test) and model discrimination (via the ROC area under the curve). For model comparisons, the Bayesian information criterion can be quite helpful in evaluating the superiority of one model over another---because BIC can be used even when models aren't nested.

 

SR Millis