In ordinary regression analysis, the coefficient of
determination (r2) is frequently used as a measure of model
performance. In logistic regression, it is common to be
more concerned with whether the predictions are correct or
incorrect than with how close the predicted values are to
the observed (0 or 1) values of the dependent variables.
Therefore, r2 has little meaning in logistic regression
analysis (Bledsoe and Watson 2001).
Goodness-of-fit tests may aid in the interpretation of the
results of logistic regression. The likelihood L0 for the null
model, where all slope parameters are zero, may be directly
compared with the likelihood L1 of the fitted model. Specifically,
one can compute the X2 statistic for this comparison
as
X2 ¼ 2ðlogðL0Þ logðL1ÞÞ ð3Þ
The degree of freedom for this X2 value is equal to the
number of independent variables in the logistic regression.
If the P-level associated with this X2 is significant, the
estimated model yields a significantly better fit to the data
than the null model and the regression parameters are
statistically significant.