[R] predict "interval" for lmRob?

[Greg Snow]

> -----Original Message-----
> From: Galkowski, Jan [mailto:jgalkows at akamai.com]
> Sent: Wednesday, April 08, 2009 12:28 PM
> To: Greg Snow; r-help at r-project.org
> Subject: RE: predict "interval" for lmRob?

[snip]

> It sounds to me like I might use the robust regression to decide what
> to discard and then apply standard linear "lm" to the remainder,
> minding the diagnostics. Should they prove favorable, I'll proceed with
> the result of "lm".

Discarding actual data points always makes me nervous.  Sometimes the points we want to discard are actually the most interesting.

> Thanks for pointing out the limitations of "robust" and its kin for me.

I consider anything that encourages me to ask questions, contemplate the answers, and really think about my data and scientific question to be a benefit rather than a limitation (one of the reasons I like R so much).

> BTW, if "robust" does not adopt a normal model for the y variable,
> what's the proper interpretation of the standard errors for slope and
> intercept it yields?  A reference?

Well there are several references on the help page for lmRob, there is also a section in MASS (the book).  But I think that while some of the techniques may have been developed for one particular distribution, it has been found that they work for a larger set of distributions and the theory does not depend on a particular distribution (you have to decide which makes the most sense for your data/application area).  For simulations to show that they work I have seen:  mixture of 2 normals, same mean but one with a much larger variance (giving the outliers), mixture of a normal and a t/cauchy, mixture of a normal and a gamma (some skewness/outliers), mixture of 2 normals with different means (outliers come from a different population mingled in with the population of interest and not easily distinguished), etc.



-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111