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I have seen Pearson residuals but I would like to know what do I gain from the information of the residuals in the sense of its magnitude? Let's say I have a residual in the size of 0.001 and one of the size 1. What does this mean? How can I use this information? Up to now I only know that it's better the lower the residual is. But how to decide which magnitude is reasonable to worry about?

Ben
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  • This is not really done, since residual magnitude depends on the data. If your data comes from a distribution with small variance then your residuals will also be small, and vice versa. – user2974951 Nov 29 '18 at 12:24
  • Thank you! So when it relates to the same data, the magnitude itself does not matter but, for example, when you compare the residuals of different models to each other? – Ben Nov 29 '18 at 12:43
  • If for ex. you were to build a linear model and a quadratic model (on the same data), then you could compare the residual magnitudes to conclude if a quadratic model better fits your data. However, as I said, this is not really done as residuals from different models (using different methodologies) are not comparable. – user2974951 Nov 29 '18 at 12:46
  • Mh, ok, thank you! So how can I then use the residuals? For the same model but different data? – Ben Nov 29 '18 at 15:58
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    @user2974951's comments are a little off-target. Pearson residuals are in effect standardized, so comparisons between residuals from different models, although rough, are not ruled out. – Nick Cox Dec 05 '18 at 16:44

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Pearson residuals are the raw residuals divided by the expected dispersion (standard deviation) assumed by the fitted model for the respective residual.

In other words: Pearson residuals quantify the difference between model / observed in units of the dispersion of the fitted model.

For a normal distribution, you expect roughly 68% of the residuals within +/-1 Pearson units, and 95% within +/- 2 Pearson units.

Florian Hartig
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  • so a pearson model is not sensitive against transformations? In my case I transformed data to a logarithmic scale and check the residuals which are quite small (10^-3). But I'm not sure what this magnitude tells me. – Ben Dec 14 '18 at 14:15