Pearson Residuals

Fit Analyses

Pearson Residuals

The Pearson residual is the raw residual divided by the square root of the variance function ${V(\mu)}$ .

The Pearson residual is the individual contribution to the Pearson $\chi^2$ statistic. For a binomial distribution with m_i trials in the ith observation, it is defined as

$r_{Pi} = \sqrt{ m_{i}} \frac{r_{i}}{\sqrt{V(\hat{ \mu_{i}})}}$

For other distributions, the Pearson residual is defined as

$r_{Pi} = \frac{r_{i}}{\sqrt{V(\hat{ \mu_{i}})}}$

The Pearson residuals can be used to check the model fit at each observation for generalized linear models. These residuals are stored in variables named RP_yname for each response variable, where yname is the response variable name.

The standardized and studentized Pearson residuals are

$r_{Psi} = \frac{r_{Pi}}{\sqrt{\hat{ \phi} (1- h_{i})} }$

$r_{Pti} = \frac{r_{Pi}}{\sqrt{ \hat{ \phi}_{(i)} (1- h_{i})} }$

The standardized Pearson residuals are stored in variables named RPS_yname and the studentized Pearson residuals are stored in variables named RPT_yname for each response variable, where yname is the response variable name.

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