psPoisson: Smoothing scattered Poisson data using P-splines.

In JOPS: Practical Smoothing with P-Splines

Smoothing scattered Poisson data using P-splines.

Description

psPoisson is used to smooth scattered Poisson data using P-splines with a log link function.

Usage

psPoisson(
  x,
  y,
  xl = min(x),
  xr = max(x),
  nseg = 10,
  bdeg = 3,
  pord = 2,
  lambda = 1,
  wts = NULL,
  show = FALSE,
  iter = 100,
  xgrid = 100
)

Arguments

x	the vector for the continuous regressor of length(y) and the abcissae used to build the B-spline basis.
y	the response vector, usually count data.
xl	the number for the min along x (default is min(x)).
xr	the number for the max along x (default is max(x)).
nseg	the number of evenly spaced segments between xl and xr (default 10).
bdeg	the number of the degree of the basis, usually 1, 2, or 3 (defalult).
pord	the number of the order of the difference penalty, usually 1, 2 (default), or 3.
lambda	the (positive) number for the tuning parameter for the penalty (default 1).
wts	the vector of general weights, zeros are allowed (default 1).
show	Set to TRUE or FALSE to display iteration history (default FALSE).
iter	a scalar to set the maximum number of iterations, default iter=100.
xgrid	a scalar or a vector that gives the x locations for prediction, useful for plotting. If a scalar (default 100) is used then a uniform grid of this size along (xl, xr).

Value

pcoef	a vector of length n of estimated P-spline coefficients.
muhat	a vector of length m of estimated means.
B	the m by n B-spline basis.
dev	deviance of fit.
effdim	effective dimension of fit.
aic	AIC.
wts	the vector of given prior weights.
nseg	the number of B-spline segments.
bdeg	the degree of the B-spline basis.
pord	the order of the difference penalty.
lambda	the positive tuning parameter.
family	the family of the response ( "Poisson").
link	the link function used ("log").
xgrid	gridded x values, useful for plotting.
ygrid	gridded fitted linear predictor values, useful for plotting.
mugrid	gridded (inverse link) fitted mean values, useful for plotting.
se_eta	gridded standard errors for the linear predictor.
dispersion	Dispersion parameter estimated dev/(m-effdim).

Author(s)

Paul Eilers and Brian Marx

References

Eilers, P.H.C. and Marx, B.D. (2021). Practical Smoothing, The Joys of P-splines. Cambridge University Press.

Eilers, P.H.C., Marx, B.D., and Durban, M. (2015). Twenty years of P-splines, SORT, 39(2): 149-186.

Examples

library(JOPS)
library(boot)

# Extract the data
Count <- hist(boot::coal$date, breaks = c(1851:1963), plot = FALSE)$counts
Year <- c(1851:1962)
xl <- min(Year)
xr <- max(Year)

# Poisson smoothing
nseg <- 20
bdeg <- 3
fit1 <- psPoisson(Year, Count, xl, xr, nseg, bdeg, pord = 2, lambda = 1)
plot(fit1, xlab = "Year", ylab = "Count", se = 2)

JOPS documentation built on Sept. 8, 2023, 5:42 p.m.