model.cons: Design and penalty matrices for the model

In survPen: Multidimensional Penalized Splines for Survival and Net Survival Models

Design and penalty matrices for the model

Description

Sets up the model before optimization. Builds the design matrix, the penalty matrix and all the design matrices needed for Gauss-Legendre quadrature.

Usage

model.cons(
  formula,
  lambda,
  data.spec,
  t1,
  t1.name,
  t0,
  t0.name,
  event,
  event.name,
  expected,
  expected.name,
  type,
  n.legendre,
  cl,
  beta.ini
)

Arguments

formula	formula object identifying the model
lambda	vector of smoothing parameters
data.spec	data frame that represents the environment from which the covariate values and knots are to be calculated
t1	vector of follow-up times
t1.name	name of t1 in data.spec
t0	vector of origin times (usually filled with zeros)
t0.name	name of t0 in data.spec
event	vector of censoring indicators
event.name	name of event in data.spec
expected	vector of expected hazard
expected.name	name of expected in data.spec
type	"net" or "overall"
n.legendre	number of nodes for Gauss-Legendre quadrature
cl	original survPen call
beta.ini	initial set of regression parameters

Value

List of objects with the following items:

cl	original survPen call
type	"net" or "overall"
n.legendre	number of nodes for Gauss-Legendre quadrature. If is.pwcst is TRUE, for simplicity of implementation, n.legendre actually corresponds to the number of sub-intervals
n	number of individuals
p	number of parameters
X.para	design matrix associated with fully parametric parameters (unpenalized)
X.smooth	design matrix associated with the penalized parameters
X	design matrix for the model
is.pwcst	TRUE if there is a piecewise constant (excess) hazard specification. In that case the cumulative hazard can be derived without Gauss-Legendre quadrature
pwcst.breaks	if is.pwcst is TRUE, vector of breaks defining the sub-intervals on which the hazard is constant. Otherwise NULL.
pwcst.weights	if is.pwcst is TRUE, matrix of weights giving the time contribution of each individual on each sub-interval. Otherwise NULL.
leg	list of nodes and weights for Gauss-Legendre integration on [-1;1] as returned by gauss.quad
X.GL	list of matrices (length(X.GL)=n.legendre) for Gauss-Legendre quadrature
S	penalty matrix for the model. Sum of the elements of S.list
S.scale	vector of rescaling factors for the penalty matrices
rank.S	rank of the penalty matrix
S.F	balanced penalty matrix as described in section 3.1.2 of (Wood,2016). Sum of the elements of S.F.list
U.F	Eigen vectors of S.F, useful for the initial reparameterization to separate penalized ad unpenalized subvectors. Allows stable evaluation of the log determinant of S and its derivatives
S.smf	List of penalty matrices associated with all "smf" calls
S.tensor	List of penalty matrices associated with all "tensor" calls
S.tint	List of penalty matrices associated with all "tint" calls
S.rd	List of penalty matrices associated with all "rd" calls
smooth.name.smf	List of names for the "smf" calls associated with S.smf
smooth.name.tensor	List of names for the "tensor" calls associated with S.tensor
smooth.name.tint	List of names for the "tint" calls associated with S.tint
smooth.name.rd	List of names for the "rd" calls associated with S.rd
S.pen	List of all the rescaled penalty matrices redimensioned to df.tot size. Every element of pen noted pen[[i]] is made from a penalty matrix returned by smooth.cons and is multiplied by the factor S.scale=norm(X,type="I")^2/norm(pen[[i]],type="I")
S.list	Equivalent to S.pen but with every element multiplied by its associated smoothing parameter
S.F.list	Equivalent to S.pen but with every element divided by its Frobenius norm
lambda	vector of smoothing parameters
df.para	degrees of freedom associated with fully parametric terms (unpenalized)
df.smooth	degrees of freedom associated with penalized terms
df.tot	df.para + df.smooth
list.smf	List of all smf.smooth.spec objects contained in the model
list.tensor	List of all tensor.smooth.spec objects contained in the model
list.tint	List of all tint.smooth.spec objects contained in the model
nb.smooth	number of smoothing parameters
Z.smf	List of matrices that represents the sum-to-zero constraints to apply for smf splines
Z.tensor	List of matrices that represents the sum-to-zero constraints to apply for tensor splines
Z.tint	List of matrices that represents the sum-to-zero constraints to apply for tint splines
beta.ini	initial set of regression parameters

Examples

library(survPen)

# standard spline of time with 4 knots

data <- data.frame(time=seq(0,5,length=100),event=1,t0=0)

form <- ~ smf(time,knots=c(0,1,3,5))

t1 <- eval(substitute(time), data)
t0 <- eval(substitute(t0), data)
event <- eval(substitute(event), data)

# The following code sets up everything we need in order to fit the model
model.c <- model.cons(form,lambda=0,data.spec=data,t1=t1,t1.name="time",
t0=rep(0,100),t0.name="t0",event=event,event.name="event",
expected=NULL,expected.name=NULL,type="overall",n.legendre=20,
cl="survPen(form,data,t1=time,event=event)",beta.ini=NULL)

survPen documentation built on Sept. 14, 2023, 1:06 a.m.