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New code in R-devel: Rao score test for glm.

6 messages · Brett Presnell, Frank E Harrell Jr, Peter Dalgaard +1 more

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I have just committed some code to the r-devel branch to implement the Rao efficient score test. This is asymptotically equivalent to the LRT, but there is some indication that it might have better properties in smaller samples since it is based more directly on the distribution of the sufficient sums under the null hypothesis (e.g., if you have a divergent fit to the model under the alternative, the chi-square distribution of the likelihood ratio may be dubious and the Wald test is surely wrong).

It works fairly obviously by using test="Rao" in various methods. See for instance the last part of example(anova.glm).

While going over the code, I took the liberty of standardizing the labeling of the p-value column to Pr(>Chi) and Pr(>F). This may break some scripts if they extract p-values using constructs like anova(glm.D93,test="Chisq")$"P(>|Chi|)"[2]. Apologies for the disturbance, but this sort of change just doesn't let itself be implemented with the usual deprecation sequence. The workaround should be straightforward (if you need something that works in multiple versions, then try both and choose the result that isn't NULL).
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Thanks for doing this Peter.  I'll have to install the development
version to try this out.

One suggestion though.  I'm pretty confident that plain old "score test"
is a more common terminology than anything involving Rao's name
(econometricians even call it the Lagrange multiplier test).  In light
of this, I think that it would be much better to use test = "score"
rather than test = "Rao".
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Economists re-invented the Rao efficient score test, calling it the Lagrange
multiplier test.  Please check the history of this test.  Rao's paper was
published in 1947.  That being said, "score" would be more consistent with
the survival and rms packages.
Frank
Brett Presnell wrote:
-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
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On May 11, 2011, at 15:10 , Brett Presnell wrote:

            
It's not like that didn't cross my mind, in fact I started out that way, but... 

- A column labeled "score" just looks odd, whereas there is some precedence for labeling tests according to authors (e.g. Pillai). 
- CR Rao is still around, now 90 years of age, and having been taught from "Linear Statistical Inference with Applications", I thought paying a little homage would be appropriate
- At least the curator calls it "Rao score test": http://www.scholarpedia.org/article/Rao_score_test

  
    
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On 2011-05-11 07:30, peter dalgaard wrote:
Yes, thanks, Peter, for coding this test.
As to the name, my vote is for "Rao".

Peter Ehlers
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I agree that homage is nice, but I really think you'll get more
confusion from "Rao" than you would from "score".  You could always
label the column some other way, right?  I mean, it doesn't have to be
exactly the same as the option.  FWIW, I also have another vote for
"score" from Alan Agresti, the only other person with whom I've
discussed this.

But I don't want to argue the point any more than that.  It seems right
for the person who wrote the code to have the final say, and I'll be
very happy to have this functionality regardless of how it's called.

Peter Ehlers <ehlers at ucalgary.ca> writes: