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The lm function in R retrieves an R^2 value.

The glm function, even if applied to a Gaussian family, does not retrieve an R^2 value.

What is/are the reason/reasons for this?

Thank you!

Ali Turab Lotia
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  • [This](https://stat.ethz.ch/pipermail/r-help/2010-June/243113.html) might help, or [this](http://stats.stackexchange.com/questions/46345/how-to-calculate-goodness-of-fit-in-glm-r) or [this](http://stats.stackexchange.com/questions/11676/pseudo-r-squared-formula-for-glms) – bdeonovic Aug 30 '16 at 11:52

1 Answers1

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The glm function uses a maximum likelihood estimator (or restricted maximum likelihood). Maximum likelihood does not minimize the squared error (this is called [ordinary] least squares). Sometimes both estimators give the same results (in the linear/ordinary case for normal distributed error terms, see here) but this does not hold in general. Since the coefficient of determination $R^2$ is calculated by ordinary least-squares regression and not by maximum likelihood, there is no reason to display this measure.

PS: Also regard Nick Cox very valid comment below: $R^2$ may be also well-definied and interesting for GLM. My personal experience is that (as so often) some people like/accept it, while others do not.

Community
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Arne Jonas Warnke
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    This is a little strong. For example, Zheng, B. and A. Agresti. 2000. Summarizing the predictive power of a generalized linear model. _Statistics in Medicine_ 19: 1771–1781 argue cogently that the square of the correlation between predicted and observed is well-defined and often interesting and useful for GLMs. It's just that some of the interpretation of $R^2$ that goes with regression is irrelevant or inappropriate in a wider context. – Nick Cox Aug 30 '16 at 12:02
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    I also warn against conflating linear regression and OLS; for example, if regression were calculated by a general maximum likelihood routine, then $R^2$ wouldn't lose validity or value. – Nick Cox Aug 30 '16 at 12:03
  • Thanks, you are right, I edited my answer in response to your comment! – Arne Jonas Warnke Aug 30 '16 at 12:16
  • Given that GLMs are fit using iteratively reweighted least squares, as in http://bwlewis.github.io/GLM/, what would be the objection actually of calculating a weighted R2 on the GLM link scale, using 1/variance weights as weights (which glm gives back in the slot weights in a glm fit)? – Tom Wenseleers Jun 11 '19 at 13:16