# [R] Intercept in lasso models

Martin Keller-Ressel martin at ist.org
Sun Apr 11 21:35:00 CEST 2004

```Hello,

Im using the function l1ce (L1-constrained estimation) from the lasso2
package.
when I try the example from the help pages

> data(Prostate)
> l1c.P <- l1ce(lpsa ~ ., Prostate, bound=.5)
> coef(l1c.P)
(Intercept)       lcavol      lweight          age         lbph
svi
0.7284810757 0.4936540169 0.2681863403 0.0000000000 0.0092825881
0.4550584943
lcp      gleason        pgg45
0.0000000000 0.0000000000 0.0001812107

everything looks fine to me. But when I use

> l1c.P <- l1ce(lpsa ~ ., Prostate, bound=(1:20)/20)
> coef(l1c.P)[10,]
(Intercept)        lcavol       lweight           age          lbph
-4.9496587740  0.4936540169  0.2681863403  0.0000000000  0.0092825881
svi           lcp       gleason         pgg45
0.4550584943  0.0000000000  0.0000000000  0.0001812107

the Intercept is different !! Also

> coef(l1c.P)[20,]
(Intercept)        lcavol       lweight           age          lbph
-23.678040866   0.587022881   0.454460641  -0.019637208   0.107054351
svi           lcp       gleason         pgg45
0.766155885  -0.105473570   0.045135964   0.004525324

should be the same as the unconstrained linear model:

> coef(lm(lpsa ~ ., data = Prostate))
(Intercept)       lcavol      lweight          age         lbph
svi
0.669399027  0.587022881  0.454460641 -0.019637208  0.107054351
0.766155885
lcp      gleason        pgg45
-0.105473570  0.045135964  0.004525324

which is true except for the Intercept...

What is going on here? Can anybody enlighten me?

Thanks,

Martin Keller-Ressel

--

```