survPen: model.cons – R documentation

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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
)

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
`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
`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

Multidimensional Penalized Splines for Survival and Net Survival Models

v1.5.1

GPL-3 | file LICENSE

Authors

Mathieu Fauvernier [aut, cre], Laurent Roche [aut], Laurent Remontet [aut], Zoe Uhry [ctb], Nadine Bossard [ctb]

Initial release