psBinomial {JOPS}

Smoothing scattered binomial data using P-splines.

Description

psBinomial is used to smooth scattered binomial data using P-splines using a logit link function.

Usage

psBinomial(
  x,
  y,
  xl = min(x),
  xr = max(x),
  nseg = 10,
  bdeg = 3,
  pord = 2,
  lambda = 1,
  ntrials = 0 * y + 1,
  wts = NULL,
  show = FALSE,
  iter = 100,
  xgrid = 100
)

Arguments

x

the vector for the continuous regressor of length(y) and the abcissae, on which the B-spline basis is constructed.

y

the response vector, usually 0/1 or binomial counts.

xl

the lower limit for the domain of x (default is min(x)).

xr

the upper limit for the domain of x (default is max(x)).

nseg

the number of evenly spaced segments between xl and xr.

bdeg

the number of the degree of the basis, usually 1, 2 (default), or 3.

pord

the number of the order of the difference penalty, usually 1, 2, or 3 (defalult).

lambda

the (positive) number for the tuning parameter for the penalty.

ntrials

the vector for the number of binomial trials (default = 1).

wts

the vector of weights, default is 1, zeros allowed.

show

Set to TRUE or FALSE to display iteration history.

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.

p

a vector of length m of estimated probabilities.

muhat

a vector of length m of estimated means (ntrials*p).

dev

deviance

effdim

effective dimension of the smooth.

aic

AIC

wts

a vector of preset weights (default = 1).

nseg

the number of B-spline segments.

bdeg

the degree of the B-spline basis.

pord

the order of the difference penalty.

family

the GLM family (repsonse distribution).

link

the link function.

y

the binomial response.

x

the regressor on which the basis is constructed.

P

"half" of the penalty matrix, P'P = lambda*D'D.

B

the B-spline basis.

lambda

the positive tuning parameter.

dispersion

dispersion parameter estimated dev/(m-effdim).

xgrid

gridded x values,useful for plotting.

ygrid

gridded fitted linear predictor values, useful for plotting.

pgrid

gridded (inverse link) fitted probability values, useful for plotting.

se_eta

gridded standard errors for the linear predictor.

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)
# Extract data
library(rpart)
Kyphosis <- kyphosis$Kyphosis
Age <- kyphosis$Age
y <- 1 * (Kyphosis == "present") # make y 0/1
fit1 <- psBinomial(Age, y,
  xl = min(Age), xr = max(Age), nseg = 20,
  bdeg = 3, pord = 2, lambda = 10
)
names(fit1)
plot(fit1, xlab = "Age", ylab = "0/1", se = 2)