Logistic Regression: variable selection based on p value?

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Puff -

There are many strategies, ideas, and literature on this topic.  A great 
introduction that leads to many of the references that are interesting 
is Frank Harrell's book, "Regression Modeling Strategies".  I would 
highly recommend it.
Hi,

When I use logistic regression, each variable has a p value associated with
it.  Do I only include the variables that have a statistically significant p
value (<0.05), or are there situations when I should include variables when
their p values are high?  I had heard that if a variable has a high p value
but it's not the terminal variable, keep it; otherwise, take it out.  Not
sure if it's right or even why this is the case.  What about if my p values
are terrible but this combo of variables yields the highest AUC and
calibration?  What prevails in this case?

Thank you!

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Hi,

When I use logistic regression, each variable has a p value associated with
it.  Do I only include the variables that have a statistically significant p
value (<0.05), or are there situations when I should include variables when
their p values are high?  I had heard that if a variable has a high p value
but it's not the terminal variable, keep it; otherwise, take it out.  Not
sure if it's right or even why this is the case.  What about if my p values
are terrible but this combo of variables yields the highest AUC and
calibration?  What prevails in this case?

Thank you!
It depends on your goals, but in general problems caused by stepwise 
regression arise from using P-value cutoffs that are too small rather 
than cutoffs that are too large.  There are many reasons not to remove 
any variables, if you want valid confidence intervals and P-values and 
discrimination indexes.  Note that AUC is not a great objective 
function; that's why we have the log likelihood.

Frank
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University