R help - Aug 2007 - The l1ce function in lasso2: The bound and absolute.t parameters.

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
S?ren

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 S?ren H?jsgaard
> Sent: Tuesday, August 28, 2007 2:03 PM
> To: r-help at stat.math.ethz.ch
> Cc: S?ren H?jsgaard; 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
> S?ren
> 
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