Deviance Residual

Definition

The deviance residual is defined as $r_{D_i}=\mathrm{sign}(y_i-{\hat{\mu }}_i)\sqrt{d_i}=\mathrm{sign}(y_i-{\hat{\mu }}_i)\sqrt{2[l{\hat{\beta }}_{\text{max}};y_i)-l\hat{\beta };y_i)]}$ where $\hat{\mu }=\mu (\theta )=b^{\prime }(\theta )$, $V(\hat{\mu })=b^{\prime \prime }(\theta )$ is the variance function, and the Deviance $D=\sum _{i=1}^n{d}_i$