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R-sq is a very common measure on goodness of fit for OLM, and many people are aware of that even with very rudimentary statistical knowledge. Is there an equivalent of R-sq for GLM (in my case, binomial/logistic)?

Thank you.

Wenwen
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  • There are pseudo r-squared measures that can be determined for generalized linear models. They are not directly analogous to r-squared, but they can be useful. – Sal Mangiafico Jul 11 '17 at 01:08
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    Firstly $R^2$ is NOT "the best" measure of goodness of fit in linear models. Sometimes it's okay but for many purposes it's often a very bad idea. Secondly, $R^2$ has a number of equivalent forms in linear models that include an intercept. but those equivalences disappear in GLMs so you need to explain what properties of the original you want and which properties you care less about. Thirdly, $R^2$ measures linear association but in generalized linear models usually the link function is non-linear ... so what are you even trying to measure? ... ctd – Glen_b Jul 11 '17 at 04:27
  • ctd... Finally there are many questions on goodness of fit in GLMs on site already -- including several in the sidebar. Please read those first, then try to formulate a clearer/ more informative question. – Glen_b Jul 11 '17 at 04:29

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For me the adj. R-square is only good for knowing whether or not your independent variables explain enough of your response. With a GLM, things are a bit more abstract since you don’t get an actual value to express this (or at least, I never learned how to do that).

However, there is the Likelihood-ratio test which shows you whether your model identifies with the null model (which basically is the equivalent of knowing whether your adj. R-sq. would be “too low” or not), and there is also the Deviance goodness of fit test which tells you whether your model identifies with the saturated model (which is the equivalent of knowing whether your adj. R-sq. value would be “high enough” or not).

PS: This post might be useful too.

Digio
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