pspline function

Univariate P-spline smoothing

Univariate P-spline smoothing with the smoothing parameter selected by leave-one-subject-out cross validation.

pspline(data, argvals.new = NULL, knots = 35,
            p = 3, m = 2, lambda = NULL,
            search.length = 100,
            lower = -20, upper = 20)

Arguments

• data: a data frame with three arguments: (1) argvals: observation times; (2) subj: subject indices; (3) y: values of observations. Missing values not allowed.
• argvals.new: a vector of observations times for prediction; if NULL, then the same as data$argvals.
• knots: a vector of interior knots or the number of knots for B-spline basis functions to be used; defaults to 35.
• p: the degrees of B-splines; defaults to 3.
• m: the order of differencing penalty; defaults to 2.
• lambda: the value of the smoothing parameter; defaults to NULL.
• search.length: the number of equidistant (log scale) smoothing parameters to search; defaults to 100.
• lower, upper: bounds for log smoothing parameter; defaults are -20 and 20.

Details

The function is an implementation of the P-spline smoothing in Eilers and Marx (1996). P-splines uses B-splines as basis functions and employs a differencing penalty on the coefficients. Leave-one-subject-out cross validation is used for selecting the smoothing parameter and a fast algorithm is implemented.

Returns

• fitted.values: Fitted mean values

• B: B-spline design matrix

• theta: Estimated coefficients

• s: Eigenvalues

• knots: Knots

• p: The degrees of B-splines

• m: The order of differencing penalty

• lambda: The value of the smoothing parameter

• argvals.new: A vector of observations times

• mu.new: Fitted mean values at argvals.new

References

Paul Eilers and Brian Marx, Flexible smoothing with B-splines and penalties, Statist. Sci., 11, 89-121, 1996.

Luo Xiao, Cai Li, William Checkley and Ciprian Crainiceanu, Fast covariance estimation for sparse functional data, Stat. Comput., tools:::Rd_expr_doi("10.1007/s11222-017-9744-8") .

Author(s)

Luo Xiao lxiao5@ncsu.edu

See Also

gam in mgcv.

Examples

## Not run:

## cd4 data
require(refund)
data(cd4)
n <- nrow(cd4)
T <- ncol(cd4)

id <- rep(1:n,each=T)
t <- rep(-18:42,times=n)
y <- as.vector(t(cd4))
sel <- which(is.na(y))

## organize data
data <- data.frame(y=log(y[-sel]),
argvals = t[-sel],
subj = id[-sel])
data <- data[data$y>4.5,]

## smooth
fit <- pspline(data)

## plot
plot(data$argvals,fit$mu.new,type="p")

## prediction
pred <- predict(fit,quantile(data$argvals,c(0.2,0.6)))
pred
## End(Not run)