# gl1ce

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

Fit a generalized regression problem while imposing an L1 constraint on
the parameters. Returns an object of class `gl1ce`

.

- Keywords
- models, regression, optimize

##### Usage

```
gl1ce(formula, data = sys.parent(), weights, subset, na.action,
family = gaussian, control = glm.control(…), sweep.out = ~ 1,
x = FALSE, y = TRUE, contrasts = NULL, standardize = TRUE,
guess.constrained.coefficients = double(p), bound = 0.5, …)
# S3 method for gl1ce
family(object, …)
```

##### Arguments

- formula
a

`formula`

, with the response on the left hand side of a`~`

operator, and the terms, separated by a`+`

operator, on the right hand side.- 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 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 be 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.- family
a

`family`

object - a list of functions and expressions for defining the link and variance functions, initialization and iterative weights. Families supported are gaussian, binomial, poisson, Gamma, inverse.gaussian and quasi. Functions like binomial produce a family object, but can be given without the parentheses. Family functions can take arguments, as in`binomial(link=probit)`

.- control
a list of iteration and algorithmic constants. See glm.control for their names and default values. These can also be set as arguments to gl1ce itself.

- 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 flag: if

`TRUE`

, the model matrix is returned in component`x`

.- y
logical flag: if

`TRUE`

, the response is 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 empirical variance one. The standardization is done after taking possible weights into account and after sweeping out variables whose parameters are not constrained.- 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.

- …
potential arguments for

`glm.control`

, as default for the`control`

argument above.- object
an R object of class

`"gl1ce"`

.

##### Value

an object of class `gl1ce`

is returned by `gl1ce()`

.
See `gl1ce.object`

for details.

##### References

See the references in `l1ce`

.

Justin Lokhorst (1999).
The LASSO and Generalised Linear Models,
Honors Project, Nov.1999, Dept.Statist., Univ. of Adelaide.
Available as file `Doc/justin.lokhorst.ps.gz`

in both shar files
from http://www.maths.uwa.edu.au/~berwin/software/lasso.html.

##### See Also

`glm`

for unconstrained generalized regression
modeling.

##### Examples

```
# NOT RUN {
## example from base:
data(esoph)
summary(esoph)
## effects of alcohol, tobacco and interaction, age-adjusted
modEso <- formula(cbind(ncases, ncontrols) ~ agegp + tobgp * alcgp)
glm.E <- glm(modEso, data = esoph, family = binomial())
gl1c.E <- gl1ce(modEso, data = esoph, family = binomial())
gl1c.E
plot(residuals(gl1c.E) ~ fitted(gl1c.E))
sg1c <- summary(gl1c.E)
sg1c
## Another comparison glm() / gl1c.E:
plot(predict(glm.E, type="link"), predict(glm.E, type="response"),
xlim = c(-3,0))
points(predict(gl1c.E, type="link"), predict(gl1c.E, type="response"),
col = 2, cex = 1.5)
# }
# NOT RUN {
<!-- %%% mabye FIXME!! -->
# }
# NOT RUN {
labels(gl1c.E)#-- oops! empty!!
# }
```

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