# l1ce

##### Regression Fitting With L1-constraint on the Parameters

Returns an object of class `"l1ce"`

or `"licelist"`

that represents
fit(s) of linear models while imposing L1 constraint(s) on the parameters.

- Keywords
- models, regression, optimize

##### Usage

```
l1ce(formula, data = sys.parent(), weights, subset, na.action,
sweep.out = ~ 1, x = FALSE, y = FALSE,
contrasts = NULL, standardize = TRUE,
trace = FALSE, guess.constrained.coefficients = double(p),
bound = 0.5, absolute.t = FALSE)
```

##### Arguments

- formula
a formula object, with the response on the left of a

`~`

operator, and the terms, separated by`+`

operators, on the right.- data
a

`data.frame`

in which to interpret the variables named in the formula, the`weights`

, the`subset`

and the`sweep.out`

argument. If this is missing, then the variables in the formula should be globally available.- weights
vector of observation weights. The length of

`weights`

must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous, compared to use of the`subset`

argument.- subset
expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.

- na.action
a function to filter missing data. This is applied to the

`model.frame`

after any`subset`

argument has been used. The default (with`na.fail`

) is to create an error if any missing values are found. A possible alternative is`na.omit`

, which deletes observations that contain one or more missing values.- sweep.out
a formula object, variables whose parameters are not put under the constraint are swept out first. The variables should appear on the right of a

`~`

operator and be separated by`+`

operators. Default is`~1`

, i.e. the constant term is not under the constraint. If this parameter is`NULL`

, then all parameters are put under the constraint.- x
logical indicating if the model matrix should be returned in component

`x`

.- y
logical indicating if the response should be returned in component

`y`

.- contrasts
a list giving contrasts for some or all of the factors appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels.

- standardize
logical flag: if

`TRUE`

, then the columns of the model matrix that correspond to parameters that are constrained are standardized to have emprical variance one. The standardization is done after taking possible weights into account and after sweeping out variables whose parameters are not constrained; see vignette for details.- trace
logical flag: if

`TRUE`

, then the status during each iteration of the fitting is reported.- guess.constrained.coefficients
initial guess for the parameters that are constrained.

- 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; see vignette for details.

##### Value

an object of class `l1ce`

(if `bound`

was a single value) or
`l1celist`

(if `bound`

was a vector of values) is returned.
See `l1ce.object`

and `l1celist.object`

for details.

##### References

Osborne, M.R., Presnell, B. and Turlach, B.A. (2000)
On the LASSO and its Dual,
*Journal of Computational and Graphical Statistics*
**9**(2), 319--337.

Tibshirani, R. (1996)
Regression shrinkage and selection via the lasso,
*Journal of the Royal Statistical Society, Series B*
**58**(1), 267--288.

##### Examples

```
# NOT RUN {
data(Iowa)
l1c.I <- l1ce(Yield ~ ., Iowa, bound = 10, absolute.t=TRUE)
l1c.I
## The same, printing information in each step:
l1ce(Yield ~ ., Iowa, bound = 10, trace = TRUE, absolute.t=TRUE)
data(Prostate)
l1c.P <- l1ce(lpsa ~ ., Prostate, bound=(1:30)/30)
length(l1c.P)# 30 l1ce models
l1c.P # -- MM: too large; should do this in summary(.)!
# }
# NOT RUN {
<!-- %% summary(l1c.P) -->
# }
# NOT RUN {
plot(resid(l1c.I) ~ fitted(l1c.I))
abline(h = 0, lty = 3, lwd = .2)
# }
```

*Documentation reproduced from package lasso2, version 1.2-20, License: GPL (>= 2)*