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I have attached an image obtained during my model validation. I fitted a negative binomial GLM to my data and I have 4 models possible with more or less the same residual plots. I have been reading about GLM as it is the first time that I use this model and it seems that if there is no pattern in the residuals the model is fine. I have to admit that I cannot really decide if my residuals follow a pattern or not. Is there a test that I could use instead of the graph? If you think that there are patterns here what can I do? I have tried Poisson and quasi poisson as well but there are clear patterns this time. My response variable is a count variable and I have both categorical and continuous covariates.

Thank you very much for your help!

enter image description here

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    $\begingroup$ That decreasing almost straight part marking the lower boundary of points on the first plot is almost certainly where $y=0$. That kind of thing is unavoidable, and that's also responsible for the apparent set of points lying on a sideways parabola in the Scale-location plot. Other than that, there's some suggestion of pattern but it's pretty mild; I'd probably want to see plots against the predictors. $\endgroup$
    – Glen_b
    Commented Jul 25, 2013 at 6:01

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Here are two tests that you could use:

  1. Whiteness Test
  2. Independence Test

In the whiteness test, if the autocorrelation function of the residuals is within the confidence interval of the estimates, then it is considered a pass.

In the Independence test, the residuals should not depend on past inputs. The Durbin-Watson statistic is used in this test.

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this is an old question, but I thought this update might be helpful: The standard R lm residuals plots don't work for GLM, but you can calculate interpretable residuals with the DHARMa package https://cran.r-project.org/web/packages/DHARMa/index.html (disclaimer: I am the developer).

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