Hello Bindu,
Thank you for taking the time to address my question.
I have been looking in the IBM SPSS Statistics Algorithms guide (SPSS V.29 p. 645) for Deviance Residuals and Studentized Residuals computation, to spot the resembles:
The Deviance calculation considers the model likelihood ratio, whereas Studentized Residuals are more probability-oriented.
I've been looking at some references online and could not find any resource that mentions that squaring the studentized residuals is similar in scale to deviance residuals.
I did find an article that, for some extent, emphasizes the differences between the measures:
https://library.virginia.edu/data/articles/understanding-deviance-residuals
On another site, I can see an example of using a deviance measure called ΔD (Hosmer et al., 2015.), Hosmer et al. (2013) and Allison (1999) that could be plotted against the predicted probabilities to find poorly fitting covariate patterns:
https://stats.oarc.ucla.edu/stat/data/logistic_regression_sas/logistic_regression_sas.html#(34)
These differences are further emphasized in other forums e.g.:
https://stats.stackexchange.com/questions/166585/pearson-vs-deviance-residuals-in-logistic-regression
Sorry for being inflexible, but how can I be sure I am using the proper interpretations of logistic regression residuals by squaring the Studentized Residuals?
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Meni Berger
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Original Message:
Sent: Thu October 03, 2024 06:56 AM
From: Bindu Krishnan
Subject: SPSS Case study seems to use the wrong measure
Hi Meni
Deviance residuals are more commonly used for evaluating the overall model fit in binary logistic regression. But studentized residuals are more commonly applied for outlier detection and influential diagnostics but are not as routinely used in the initial assessment of model fit. Usually logistic regression output focuses on deviance residuals when examining model diagnostics, but both can be useful depending on our specific needs ,that is, based on the context of fitting assessment as well as outlier detection.
The deviance residuals are the squared transformations (in terms of deviance contributions), making them inherently linked to the deviance measure used in logistic regression. However, studentized residuals are not squared by default. Squaring them allows the studentized residuals to be used in a context where they can represent a change in deviance, providing a common scale for comparing different observations. In other words, the deviance residuals reflect the contribution to the deviance for each observation while the studentized residuals reflect how far an observation's prediction is from its expected value after accounting for variance. So, when we square the studentized residuals, we essentially give them a similar scale to deviance residuals, allowing for comparison. This enables us to see how much each observation contributes to the model fit in a form analogous to a change in deviance for that data point. Squaring the studentized residuals and plotting them against the predicted probabilities helps in visualizing patterns of misfit and identifying outliers. By squaring the studentized residuals, we can observe how certain predicted probabilities correspond to greater deviations from the model's fit.
Regards
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Bindu Krishnan
Senior Statistician
IBM SPSS Statistics
Original Message:
Sent: Tue October 01, 2024 07:34 AM
From: Meni Berger
Subject: SPSS Case study seems to use the wrong measure
Hello group!
I was reading the SPSS Documentation in the knowledge center. specifically, a case study for logistic regression. On this link the instruction refers the user to save Studentized Residuals in the logistic: save dialogue. On this link, the user is instructed to square the Studentized Residuals to plot them with the predicted probabilities as changed deviance scores.
As far as I know the Studentized Residuals are not Deviant Residuals, and the latter is used specifically for logistic regression.
Does someone know why SPSS Documentation is referring Studentized Residuals as Deviant Residuals?
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Meni Berger
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