survPen (version 2.0.1)

smf: Defining smooths in survPen formulae

Description

Used inside a formula object to define a smooth, a tensor product smooth or a tensor product interaction. Natural cubic regression splines (linear beyond the knots, equivalent to ns from package splines) are used as marginal bases. While tensor builds a tensor product of marginal bases including the intercepts, tint applies a tensor product of the marginal bases without their intercepts. Unlike tensor, the marginal effects of the covariates should also be present in the formula when using tint. For a conceptual difference between tensor products and tensor product interactions see Section 5.6.3 from Wood (2017)

Usage

smf(..., knots = NULL, df = NULL, by = NULL, same.rho = FALSE)
tensor(..., knots = NULL, df = NULL, by = NULL, same.rho = FALSE)
tint(..., knots = NULL, df = NULL, by = NULL, same.rho = FALSE)

Value

object of class smf.smooth.spec, tensor.smooth.spec or tint.smooth.spec (see smooth.spec for details)

Arguments

...

Any number of covariates separated by ","

knots

numeric vector that specifies the knots of the splines (including boundaries); default is NULL, in which case the knots are spread through the covariate values using quantiles. Precisely, for the term "smf(x,df=df1)", the vector of knots will be: quantile(unique(x),seq(0,1,length=df1))

df

numeric value that indicates the number of knots (or degrees of freedom) desired; default is NULL. If knots and df are NULL, df will be set to 10

by

numeric or factor variable in order to define a varying coefficient smooth

same.rho

if the specified by variable is a factor, specifies whether the smoothing parameters should be the same for all levels; default is FALSE.

References

Wood, S. N. (2017), Generalized additive models: an introduction with R. Second Edition. London: Chapman & Hall/CRC.

Examples

# penalized cubic regression spline of time with 5 unspecified knots
formula.test <- ~smf(time,df=5)

# suppose that we want to fit a model from formula.test
library(survPen)
data(datCancer)

mod.test <- survPen(~smf(fu,df=5) ,data=datCancer,t1=fu,event=dead)

# then the knots can be retrieved like this:
mod.test$list.smf[[1]]$knots
# or calculated like this
quantile(unique(datCancer$fu),seq(0,1,length=5))


# penalized cubic regression splines of time and age with respectively 5 and 7 unspecified knots
formula.test2 <- ~smf(time,df=5)+smf(age,df=7)

# penalized cubic regression splines of time and age with respectively 3 and 4 specified knots
formula.test3 <- ~smf(time,knots=c(0,3,5))+smf(age,knots=c(30,50,70,90))

# penalized tensor product for time and age with respectively 5 and 4 unspecified knots leading
# to 5*4 = 20 regression parameters
formula.test <- ~tensor(time,age,df=c(5,4))

# penalized tensor product for time and age with respectively 3 and 4 specified knots
formula.test3 <- ~tensor(time,agec,knots=list(c(0,3,5),c(30,50,70,90)))

# penalized tensor product for time, age and year with respectively 6, 5 and 4 unspecified knots
formula.test <- ~tensor(time,age,year,df=c(6,5,4))

# penalized tensor product interaction for time and age with respectively 5 and 4 unspecified knots
# main effects are specified as penalized cubic regression splines
formula.test <- ~smf(time,df=5)+smf(age,df=4)+tint(time,age,df=c(5,4))