First I'm a little bit confused with the assumptions of a model with binomial response and logit link function. Since it is basically a logistic regression. Today one of my professors told me that I had to prove normality of my residuals, but of what I know the assumptions are:

First, binary logistic regression requires the dependent variable to be binary and ordinal logistic regression requires the dependent variable to be ordinal.

Second, logistic regression requires the observations to be independent of each other. In other words, the observations should not come from repeated measurements or matched data.

Third, logistic regression requires there to be little or no multicollinearity among the independent variables. This means that the independent variables should not be too highly correlated with each other.

Also these are the plots I have: enter image description here

enter image description here

So basically my question is: what assumptions can I prove/not prove with these plots?

  • $\begingroup$ What do you think the top-left chart suggests? $\endgroup$ – Henry Dec 14 '19 at 0:30
  • $\begingroup$ It's close to normality if I only see it with plot. But when I use the shapiro wilk test It says that's it's not normally distributed. But then I don't know if I have to use the residuals or the transformation of the residuals (because i'm using the logit link function) EDIT: It was left! sorry i did the right. $\endgroup$ – Lexie Walker Dec 14 '19 at 0:35
  • $\begingroup$ If I'm not wrong the top left indicates a tendency, but I don't know if the tendency is because of my response variable. $\endgroup$ – Lexie Walker Dec 14 '19 at 0:40
  • $\begingroup$ In what context did your professor say you need normal residuals? That’s a pretty incorrect claim for logistic regression. $\endgroup$ – Dave Dec 14 '19 at 15:40

There is no normal assumption in logistic regression, so why would you want to check normality of residuals? There is more information here: Interpreting residual diagnostic plots for glm models?

See also What to do with GLM (Gamma) when residuals are not normally distributed? for understanding the residuals in glm's (generalized linear models) such as logistic regression better.

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  • $\begingroup$ But here stats.stackexchange.com/questions/32285/… the person who answered said that it was important to check the normality of the residuals in glm. $\endgroup$ – Lexie Walker Dec 14 '19 at 18:14
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    $\begingroup$ If you look further at that post, it is about a gaussian glm with identity link. Thas is, old linear regression. That advice do not extend to logistic regression. Remember that glm is a family of models, and what is right for one member is not necessarily right for others. $\endgroup$ – kjetil b halvorsen Dec 15 '19 at 0:24

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