Fit a Cox regression model via penalized maximum likelihood for a single value of lambda. Can deal with (start, stop] data and strata, as well as sparse design matrices.
multiview.cox.fit(
x_list,
x,
y,
rho,
weights,
lambda,
alpha = 1,
offset = rep(0, nobs),
thresh = 1e-10,
maxit = 1e+05,
penalty.factor = rep(1, nvars),
exclude = c(),
lower.limits = -Inf,
upper.limits = Inf,
warm = NULL,
from.cox.path = FALSE,
save.fit = FALSE,
trace.it = 0
)An object with class "coxnet", "glmnetfit" and "glmnet". The list returned contains more keys than that of a "glmnet" object.
Intercept value, NULL for "cox" family.
A nvars x 1 matrix of coefficients, stored in sparse matrix
format.
The number of nonzero coefficients.
Dimension of coefficient matrix.
Lambda value used.
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.
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.
If save.fit=TRUE, output of C++ routine, used for
warm starts. For internal use only.
Family used for the model, always "cox".
A logical variable: was the algorithm judged to have converged?
A logical variable: is the fitted value on the boundary of the attainable values?
Objective function value at the solution.
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 single value for the lambda hyperparameter.
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.
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.
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.
Maximum number of passes over the data for all lambda values; default is 10^5.
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.
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.
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
Either a glmnetfit object or a list (with names beta
and a0 containing coefficients and intercept respectively) which can
be used as a warm start. Default is NULL, indicating no warm start.
For internal use only.
Was multiview.cox.fit() called from multiview.path()?
Default is FALSE.This has implications for computation of the penalty factors.
Return the warm start object? Default is FALSE.
If trace.it=1, then a progress bar is
displayed; useful for big models that take a long time to fit.
WARNING: Users should not call multiview.cox.fit directly. Higher-level
functions in this package call multiview.cox.fit as a subroutine. If a
warm start object is provided, some of the other arguments in the function
may be overriden.
multiview.cox.fit solves the elastic net problem for a single, user-specified
value of lambda. multiview.cox.fit works for Cox regression models, including
(start, stop] data and strata. It solves the problem using iteratively
reweighted least squares (IRLS). For each IRLS iteration, multiview.cox.fit
makes a quadratic (Newton) approximation of the log-likelihood, then calls
elnet.fit to minimize the resulting approximation.
In terms of standardization: multiview.cox.fit does not standardize x
and weights. penalty.factor is standardized so that they sum
up to nvars.