[R] Cook's distance for least absolute deviation (lad) regressions

[John Fox]

Dear Kelly and Jim,

On 2022-03-20 9:40 p.m., Jim Lemon wrote:
> Hi Kelly,
> Perhaps the best place to look is the "car" package. There is a
> somewhat confusing reference in the "cookd" function help page to the
> "cooks.distance" function in the "base" package that doesn't seem to
> be there.  Whether this is the case or not, I think you can still use
> the "cookd" alias.

cookd() in the car package has been defunct for some time.

To address the original question: One can compute Cook's distances for 
*any* regression model by brute-force, omitting each case i in turn and 
computing the Wald F or chisquare test statistic for the "hypothesis" 
that the deleted estimate of the regression coefficients b_{-i} is equal 
to the estimate b for all of the data. In a linear model, D can be 
computed much more efficiently based on the hatvalues, etc., without 
having to refit the model n times, but that's not generally the case, 
unless the model can be linearized (as for a GLM fit by IWLS).

I'm insufficiently familiar with the computational details of LAD 
regression (or quantile regression more generally) to know whether a 
more efficient computation is possible there, but unless the data set is 
very large, in which case it's highly unlikely that influence of 
individual cases is an issue, the brute-force approach should be 
feasible and very easy to program.

I hope this helps,
  John

-- 
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://socialsciences.mcmaster.ca/jfox/

> 
> Jim
> 
> On Mon, Mar 21, 2022 at 11:57 AM Kelly Thompson <kt1572757 using gmail.com> wrote:
>>
>> I'm wanting to calculate Cook's distance for least absolute deviation
>> (lad) regressions.
>>
>> Which R packages and functions offer this?
>>
>> Thanks!
>>
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> 
> ______________________________________________
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