[R] The l1ce function in lasso2: The bound and absolute.tparameters.

Greg Snow Greg.Snow at intermountainmail.org
Wed Aug 29 16:54:19 CEST 2007

This is my understanding of what is happening.

1. Standardize all the x variables to have mean 0 and variance 1 (possibly y as well).
2. Compute the unconstrained least squares regression.
3. Sum the abs values of the b's.

That sum is the scaling factor.  A bound of 1 means the sum above (and any bound greater than that will just give the same unconstrained results).  A bound of 0.5 means half of the sum above, etc.

Hope this helps,

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Søren Højsgaard
> Sent: Tuesday, August 28, 2007 2:03 PM
> To: r-help at stat.math.ethz.ch
> Cc: Søren Højsgaard; steffen at stats.ox.ac.uk
> Subject: [R] The l1ce function in lasso2: The bound and 
> absolute.tparameters.
> Dear all,
> I am quite puzzled about the bound and absolute.t arguments 
> to the l1ce function in the lasso2 package. (The l1ce 
> function estimates the regression parameter b in a regression 
> model y=Xb+e subject to the constraint that |b|<t for some value t).
> The doc says:
> bound	 numeric, either a single number or a vector: the 
> constraint(s) that is/are put onto the L1 norm of the parameters.	
> absolute.t	 logical flag: if TRUE, then bound is an 
> absolute bound and all entries in bound can be any positive 
> number. If FALSE, then bound is a relative bound and all 
> entries must be between 0 and 1.	
> Default is that bound=0.5 and absolute.t is FALSE. Hence the 
> bound is relative to "something", but I can't figure out what 
> this "something" is (and it is not clear from the papers 
> listed in the man pages either). Can anyone help on this??
> Thanks
> Søren
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