Deviance Chi-Squared Test

The deviance $\chi^2$ value is,

where $g$ is the number of replicate groups in the design, $n_i$ is the number of runs, $y_i$ is the number of successes (1s), and $\hat{\pi}_i$ is the predicted probability in the $i^{th}$ replicate group.

The degrees of freedom for the test is the number of replicate groups minus the number of parameters $p$ in the model, $df = g - p$.

There is evidence of poor fit if the $\chi^2$ value per degree of freedom, $D/df = D/(g-p)$, differs significantly from 1 or the p-value is less than the $\alpha$-risk.

If the design contains few replicates use the Hosmer-Lemeshow test instead.

References