cSFM (version 1.1)

kpbb: Kronecker Product Bspline Basis

Description

Generate the B-spline basis matrix for a polynomial spline, applicable for both univariate basis and bivariate basis systems.

Usage

kpbb(tp, cp = NULL, nknots.tp, nknots.cp = NULL,  sub.case = 2, degree.poly = 3)

Arguments

tp

timepoint vector in the time direction; must be sorted

cp

covariate vector in the covariate direction; must be sorted

nknots.tp

number of knots for the time direction; See 'Details'

nknots.cp

number of knots for the covariate direction; See 'Details'

sub.case

indicator for univariate (sub.case = 1) or bivariate (sub.case = 2)

degree.poly

degree of polynomials for B-spline basis system; default is 3, i.e. cubis splines

Value

A basis matrix, with attributes which are for the future use of predict.kpbb.

Details

kpbb is built based on the function bs. For the time direction, the generated basis matrix has the dimension length(tp) by nknots.tp + degree.poly + 1, regardless whehter the number of knots is negative or not. When sub.case = 2, the generated basis matrix is the kronecker product of the two basis matrices.

References

[1]. Meng Li, Ana-Maria Staicu and Howard D. Bondell (2013), Incorporating Covariates in Skewed Functional Data Models. http://www.stat.ncsu.edu/information/library/papers/mimeo2654_Li.pdf.

See Also

bs, predict.kpbb, data.simulation

Examples

data(data.simulation) # load benchmark data 
y <- DST$obs # matrix of observation
# generate bivariate basis using 3 knots for each direction
basis <- kpbb(DST$tp, DST$cp, nknots.tp = 3, nknots.cp = 3)
# linear regression
lm.fit <- lm(as.vector(y) ~ basis - 1)
y.fit <- matrix(fitted(lm.fit), nrow = 100, ncol = 80)

# visualize the data and fitted surface
par(mfrow = c(1,2))
persp(DST$cp, DST$tp, y, theta=60, phi=15,
      ticktype = "detailed", col="lightblue", 
      xlab = "covariate", ylab = "time",
      zlab="data", main="data surface")
persp(DST$cp, DST$tp, y.fit, theta=60, phi=15,
      ticktype = "detailed", col="lightblue", 
      xlab = "covariate", ylab = "time",
      zlab="data", main="fitted surface via lm")