From: A comparison of residual diagnosis tools for diagnosing regression models for count data
Model | Pearson residuals |
---|---|
Poisson | \(r^{P}_{i} = \frac {y_{i}-\hat {\lambda }_{i}}{\sqrt {\hat {\lambda }_{i}}}\) |
NB | \(r^{P}_{i} = \frac {y_{i}-\hat {\lambda }_{i}}{\sqrt {\hat {\lambda }_{i}+\hat {\lambda }_{i}^{2}/k}}\) |
ZIP | \(r^{P}_{i} = \frac {y_{i}-\left (1-\hat {p}_i \right)\hat {\lambda }_i}{\sqrt {\left (1-\hat {p}_i \right)\hat {\lambda }_i \left [ 1+\hat {p}_i \hat {\lambda }_i \right ]}}\) |
ZINB | \(r^{P}_{i} = \frac {y_{i}-(1-\hat p_{i})\hat \lambda _{i}}{\sqrt {(1-\hat p_{i})\left (\hat \lambda _{i}+\frac {{\hat \lambda _{i}}^{2}}{k}\right)+{\hat \lambda _{i}}^{2} \left ({\hat p_{i}}^{2}+\hat p_{i}\right)}}\) |