model.cons: 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
)

Value

List of objects with the following items:

cl: original survPen call
type: "net", "overall", or "mult"
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

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

Examples

Run this code


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=rep(0,100),expected.name=NULL,type="overall",n.legendre=20,
cl="survPen(form,data,t1=time,event=event)",beta.ini=NULL)

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