Fit a Cox regression model via penalized maximum likelihood for a path of lambda values. Can deal with (start, stop] data and strata, as well as sparse design matrices.
multiview.cox.path(
x_list,
x,
y,
rho = 0,
weights = NULL,
lambda = NULL,
offset = NULL,
alpha = 1,
nlambda = 100,
lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
standardize = TRUE,
intercept = TRUE,
thresh = 1e-07,
exclude = integer(0),
penalty.factor = rep(1, nvars),
lower.limits = -Inf,
upper.limits = Inf,
maxit = 1e+05,
trace.it = 0,
nvars,
nobs,
xm,
xs,
control,
vp,
vnames,
is.offset
)An object of class "coxnet" and "glmnet".
Intercept value, NULL for "cox" family.
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 0 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.
Number of observations.
a list of x matrices with same number of rows
nobs
the cbinded matrices in x_list
the quantitative response with length equal to nobs, the
(same) number of rows in each x matrix
the weight on the agreement penalty, default 0. rho=0
is a form of early fusion, and rho=1 is a form of late fusion.
We recommend trying a few values of rho including 0, 0.1, 0.25,
0.5, and 1 first; sometimes rho larger than 1 can also be
helpful.
observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation
A user supplied lambda sequence, default
NULL. Typical usage is to have the program compute its own
lambda sequence. This sequence, in general, is different from
that used in the glmnet::glmnet() call (named lambda)
Supplying a value of lambda overrides this. WARNING: use with
care. Avoid supplying a single value for lambda (for
predictions after CV use stats::predict() instead. Supply
instead a decreasing sequence of lambda values as multiview
relies on its warms starts for speed, and its often faster to fit
a whole path than compute a single fit.
A vector of length nobs that is included in
the linear predictor (a nobs x nc matrix for the
"multinomial" family). 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.
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.
The number of lambda values - default is 100.
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
"binomial" and "multinomial" models, and
glmnet will exit gracefully when the percentage deviance
explained is almost 1.
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. See details below for
y standardization with family="gaussian".
Should intercept(s) be fitted (default TRUE)
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. Defaults value is
1E-7.
Indices of variables to be excluded from the
model. Default is none. Equivalent to an infinite penalty factor
for the variables excluded (next item). Users can supply instead
an exclude function that generates the list of indices. This
function is most generally defined as function(x_list, y, ...),
and is called inside multiview to generate the indices for
excluded variables. The ... argument is required, the others
are optional. This is useful for filtering wide data, and works
correctly with cv.multiview. See the vignette 'Introduction'
for examples.
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, and the
lambda sequence will reflect this change.
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
Vector of upper limits for each coefficient;
default Inf. See lower.limits
Maximum number of passes over the data for all lambda values; default is 10^5.
If trace.it=1, then a progress bar is
displayed; useful for big models that take a long time to fit.
the number of variables (total)
the number of observations
the column means vector (could be zeros if standardize = FALSE)
the column std dev vector (could be 1s if standardize = FALSE)
the multiview control object
the variable penalities (processed)
the variable names
a flag indicating if offset is supplied or not
Sometimes the sequence is truncated before nlambda values of lambda
have been used. This happens when cox.path detects that the
decrease in deviance is marginal (i.e. we are near a saturated fit).
set.seed(2)
nobs <- 100; nvars <- 15
xvec <- rnorm(nobs * nvars)
xvec[sample.int(nobs * nvars, size = 0.4 * nobs * nvars)] <- 0
x <- matrix(xvec, nrow = nobs)
beta <- rnorm(nvars / 3)
fx <- x[, seq(nvars / 3)] %*% beta / 3
ty <- rexp(nobs, exp(fx))
tcens <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv <- survival::Surv(ty, tcens)
fit1 <- glmnet:::cox.path(x, jsurv)
# works with sparse x matrix
x_sparse <- Matrix::Matrix(x, sparse = TRUE)
fit2 <- glmnet:::cox.path(x_sparse, jsurv)
# example with (start, stop] data
set.seed(2)
start_time <- runif(100, min = 0, max = 5)
stop_time <- start_time + runif(100, min = 0.1, max = 3)
status <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv_ss <- survival::Surv(start_time, stop_time, status)
fit3 <- glmnet:::cox.path(x, jsurv_ss)
# example with strata
jsurv_ss2 <- glmnet::stratifySurv(jsurv_ss, rep(1:2, each = 50))
fit4 <- glmnet:::cox.path(x, jsurv_ss2)
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