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I read on this page, that residual plots can be used to determine whether or not a linear model for regression is suitable. I am working on a binary classification problem, with the classes 0 and 1. In the project I used various models and measured the quality of the fit. Just out of curiosity and for future uses, I'd like to know if I can use residual plots to decide whether or not logistic regression is a good choice and if so, how?

Since the result of a linear regression is taken as input to the logistic function in logistic regression, I thought maybe I could take the calculated probabilities and apply an inverse function of the logistic function to them. This way I should get back the results of the internal linear regression. However since I want residuals, I'd only have zeros and ones to compare those linear regression results with. I could then still plot the differences between labels and linear regression results. Would that be a way to use residual to determine if logistic regression could be a good choice?

(all assuming no feature engineering for now)

So far I've only tried some models when I had to do some classification, but it wouldn't be bad to know a more systematic approach to figuring out what model to use and why others are not so appropriate. Residual plots seem to provide that for linear regression, as far as I understand.

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