Fit a generalized linear model via penalized maximum likelihood for a path of lambda values. Can deal with any GLM family.

```
glmnet.path(
x,
y,
weights = NULL,
lambda = NULL,
nlambda = 100,
lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
alpha = 1,
offset = NULL,
family = gaussian(),
standardize = TRUE,
intercept = TRUE,
thresh = 1e-10,
maxit = 1e+05,
penalty.factor = rep(1, nvars),
exclude = integer(0),
lower.limits = -Inf,
upper.limits = Inf,
trace.it = 0
)
```

x

Input matrix, of dimension `nobs x nvars`

; each row is an
observation vector. Can be a sparse matrix.

y

Quantitative response variable.

weights

Observation weights. Default is 1 for each observation.

lambda

A user supplied lambda sequence. Typical usage is to have the
program compute its own lambda sequence based on `nlambda`

and
`lambda.min.ratio`

. Supplying a value of lambda overrides this.

nlambda

The number of lambda values, default is 100.

lambda.min.ratio

Smallest value for lambda as a fraction of lambda.max,
the (data derived) entry value (i.e. the smallest value for which all
coefficients are zero). The default depends on the sample size `nobs`

relative to the number of variables `nvars`

. If `nobs >= nvars`

, the
default is 0.0001, close to zero. If `nobs < nvars`

, the default is 0.01.
A very small value of `lambda.min.ratio`

will lead to a saturated fit
in the `nobs < nvars`

case. This is undefined for some families of
models, and the function will exit gracefully when the percentage deviance
explained is almost 1.

alpha

The elasticnet mixing parameter, with \(0 \le \alpha \le 1\).
The penalty is defined as $$(1-\alpha)/2||\beta||_2^2+\alpha||\beta||_1.$$
`alpha=1`

is the lasso penalty, and `alpha=0`

the ridge penalty.

offset

A vector of length `nobs`

that is included in the linear
predictor. Useful for the "poisson" family (e.g. log of exposure time), or
for refining a model by starting at a current fit. Default is NULL. If
supplied, then values must also be supplied to the `predict`

function.

family

A description of the error distribution and link function to be
used in the model. This is the result of a call to a family function. Default
is `gaussian()`

. (See `family`

for details on
family functions.)

standardize

Logical flag for x variable standardization, prior to
fitting the model sequence. The coefficients are always returned on the
original scale. Default is `standardize=TRUE`

. If variables are in the
same units already, you might not wish to standardize.

intercept

Should intercept be fitted (default=TRUE) or set to zero (FALSE)?

thresh

Convergence threshold for coordinate descent. Each inner
coordinate-descent loop continues until the maximum change in the objective
after any coefficient update is less than thresh times the null deviance.
Default value is `1e-10`

.

maxit

Maximum number of passes over the data; default is `10^5`

.

penalty.factor

Separate penalty factors can be applied to each
coefficient. This is a number that multiplies `lambda`

to allow differential
shrinkage. Can be 0 for some variables, which implies no shrinkage, and that
variable is always included in the model. Default is 1 for all variables (and
implicitly infinity for variables listed in exclude). Note: the penalty
factors are internally rescaled to sum to `nvars`

.

exclude

Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor.

lower.limits

Vector of lower limits for each coefficient; default
`-Inf`

. Each of these must be non-positive. Can be presented as a single
value (which will then be replicated), else a vector of length `nvars`

.

upper.limits

Vector of upper limits for each coefficient; default
`Inf`

. See `lower.limits`

.

trace.it

Controls how much information is printed to screen. Default is
`trace.it=0`

(no information printed). If `trace.it=1`

, a progress
bar is displayed. If `trace.it=2`

, some information about the fitting
procedure is printed to the console as the model is being fitted.

An object with class "glmnetfit" and "glmnet".

Intercept sequence of length `length(lambda)`

.

A `nvars x length(lambda)`

matrix of coefficients, stored in
sparse matrix format.

The number of nonzero coefficients for each value of lambda.

Dimension of coefficient matrix.

The actual sequence of lambda values used. When alpha=0, the largest lambda reported does not quite give the zero coefficients reported (lambda=inf would in principle). Instead, the largest lambda for alpha=0.001 is used, and the sequence of lambda values is derived from this.

The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the intercept model.

Total passes over the data summed over all lambda values.

Error flag, for warnings and errors (largely for internal debugging).

A logical variable indicating whether an offset was included in the model.

The call that produced this object.

Family used for the model.

Number of observations.

`glmnet.path`

solves the elastic net problem for a path of lambda values.
It generalizes `glmnet::glmnet`

in that it works for any GLM family.

Sometimes the sequence is truncated before `nlambda`

values of lambda
have been used. This happens when `glmnet.path`

detects that the decrease
in deviance is marginal (i.e. we are near a saturated fit).

```
# NOT RUN {
set.seed(1)
x <- matrix(rnorm(100 * 20), nrow = 100)
y <- ifelse(rnorm(100) > 0, 1, 0)
# binomial with probit link
fit1 <- glmnet:::glmnet.path(x, y, family = binomial(link = "probit"))
# }
```

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