[R] Hosmer-Lemeshow 'goodness of fit'

[Frank Harrell]

The test in the rms package's residuals.lrm function is the le Cessie - van
Houwelingen - Copas - Hosmer unweighted sum of squares test for global
goodness of fit.  Like all statistical tests, a large P-value has no
information other than there was not sufficient evidence to reject the null
hypothesis.  Here the null hypothesis is that the true probabilities are
those specified by the model.  Such an omnibus test, though having good
general power (better than Hosmer-Lemeshow) lacks power to detect specific
alternatives.  That's why I spend more time allowing for nonlinearity of
predictors.

Frank


viostorm wrote:
> 
> Again, thanks so much for your help.
> 
> Is there a "for dummies" version for interpreting the le Cessie and
> Houwelingen test.  I read the 1991 biometrics paper but honestly got lost
> in the math.
> 
> Is it interpreted the same way the Hosmer-Lemeshow test is?  ie, a
> non-significant result means model fits well.   
> 
> I guess what does, what would my p-value of p=0.284362 tell you about my
> model?  
> 
> I would like to describe the goodness of fit of my model in a paper but
> I'm worried the average medical reader would not know how to interpret the
> result of this test whereas there are lots of references on interpreting
> Hosmer-Lemeshow.
> 
> (my cross validated c-statistic was 0.69 and r^2 was 0.15)
> 
> Thanks again for your all help! (also with my k-fold crossvalidation
> question!)
> 
> -Rob
> 
> -------------------------------- 
> Robert Schutt, MD, MCS 
> Resident - Department of Internal Medicine 
> University of Virginia, Charlottesville, Virginia
> 


-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
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