Residual concerns

(Jun 5, 2009)

One of the most important means of checking a model's fit is to look at the residuals, i.e. the standardised differences between the actual data observed and what the model predicts.  One common definition, known as the Pearson residual, is as follows:

Definition of Pearson residual

where r is the residual, D is the observed number of deaths and E is the expected number of deaths. This definition is quick and easy to apply, and works well where there are relatively large numbers of observed and expected deaths.  If the underlying model used to generate the expected values in E is correct, the residuals should have an approximate N(0, 1) distribution.  The sum of the r2 values can be compared with the appropriate point of a χ2 (chi-squared)

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Tags: residual, deviance residual, Pearson residual

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