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I am trying to fit a model estimating the success probability of the Bernoulli distributed random variable with the logistic link function.

However, I am stuck with testing the goodness of fit of my model.

I know I cannot use the usual chi-squared test, which compares "LRT statistic for a test with null parameter space of dimension p and the alternative of dimension n(saturated model)" with (n-p) chi-squared distribution since asymptotic normality of the parameter of a saturated model cannot be achieved. Also, the note says that "For Bernoulli and binomial models with small counts we cannot expect both Pearson and Deviance residuals to be Normal".

At this stage, it seems all I can look at is Cook`s distance. How could I perform any further goodness of fit test/residual analysis in this case then? Are there any other general methods that I am not aware of?

kjetil b halvorsen
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wruskrappy
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  • Where do those quotes come from? – gung - Reinstate Monica Jan 17 '19 at 14:33
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    Here are some of my prior answers that might help get you going. Goodness / lack of fit in a logistic regression context: [Understanding lack of fit in logistic regression](https://stats.stackexchange.com/a/233826/7290); testing / seeing / understanding lack of fit in a concrete example: [Test logistic regression model using residual deviance and degrees of freedom](https://stats.stackexchange.com/a/248978/7290); & some plots / EDA for logistic regression: [Any necessary EDA before logistic?](https://stats.stackexchange.com/a/250513/7290) – gung - Reinstate Monica Jan 17 '19 at 14:37
  • The quotes are from the lecture notes and lecture slides. And thank you very much for the links. – wruskrappy Jan 17 '19 at 15:19

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