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I was hoping someone would be able to help me understand this - I have calculated Nagelkerke's R2 for the generalised linear model results with covariates included. ie:

dependent variable ~ independent variable + covariate 1 + covariate 2

I then calculated Nagelkerke's R2 from the null model (just the model with covariates):

dependent variable ~ covariate 1 + covariate 2

The R2 value from the full model was 0.20. The R2 value from the null model was 0.12. Does that mean that the independent variable in the full model explains ~ 8% of variance?

Heather Harrington
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Nagelkerke's $R^2$ is a function the likelihood of the two models, not the variance, so you cannot say anything about the variance through Nagelkerke's $R^2$. The paper A note on a general definition of the coefficient of determination is short and quite easy to read, and in the context of your question, the important part is the definition for Cox&Snell's $R^2$

$$ R^2 = 1-\{L(0)/L(\hat{\beta})\}^{2/n} $$

where $L(0)$ and $L(\hat{\beta})$ are the log likelihoods of the null and the fitted models. The log likelihood measures the goodness of fit of a model to the data. Nagelkerke proposed using $R^2/max(R^2)$, for reasons listed in the paper.

There is no easy and intuitive interpretation of Nagelkerke's $R^2$ that at the same time is precise - only the definition itself, which is not easy and intuitive, and vague statements about increase in goodness of fit.

kajsam
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