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What kind of test in summary(glm)?

3 messages · Anne Morgenstern, Brian Ripley, Frank E Harrell Jr

Anne Morgenstern
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Hello R Users,

when I use summary(glm) for a logistic regression model with logit as link
function I get one column "z value". What kind of test does R use? (I would
have expected a t-test).

Thanks, Anne
Brian Ripley
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On Wed, 10 Oct 2001, Anne Morgenstern wrote:

            

      
      
      
    

        
It's not doing a test at all.  It is reporting a z value, the coefficient
divided by the estimated standard error.  Now although that is often
called a `t value', it is not for a GLM (except in special cases)
t-distributed under the null hypothesis.  If you mean that you used
glm(family=binomial), the scale is not estimated and the relevant
asymptotic theory suggests a normal distribution.  However, that can be
rather misleading.  Under glm(family=pseudobinomial) the scale is
estimated, but there is no really relevant theory (as you have a
quasi-likelihood model) suggesting a t distribution.

If you want to test, use anova.glm not the Wald statistic given by the
`z value', because of the Hauck-Donner effect.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Frank E Harrell Jr
    

    

      
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To go a bit farther, simulations have shown that a t
distribution is inappropriate because it is overly
conservative (due to not having to estimate sigma).
P-values using the normal distribution are more
accurate than those from t.

As Brian noted, the Hauck-Donner effect can ruin
Wald statistics.  When a variable does not have
a dominating effect (i.e., when there is no cell
containing less than perhaps two observations
but this depends on N) Wald stats work reasonably
well.

Frank Harrell

        
Prof Brian Ripley wrote: