JOPS (version 0.2.0)

psPoisson: 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
)

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).

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).

Author

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)