sgplm1: Generalized partial linear model

In gplm: Generalized Partial Linear Models (GPLM)

Description

Fits a generalized partial linear model (based on smoothing spline) using the (generalized) Speckman estimator or backfitting (in the generalized case combined with local scoring) for two additive component functions. In contrast to kgplm, this function can be used only for a 1-dimensional nonparametric function.

Usage

sgplm1(x, t, y, spar, df=4, family, link,
       b.start=NULL, m.start=NULL, grid = NULL, offset = 0, 
       method = "speckman", weights = 1, weights.trim = 1, 
       weights.conv = 1, max.iter = 25, eps.conv = 1e-8,
       verbose = FALSE, ...)

Arguments

x	n x p matrix, data for linear part
y	n x 1 vector, responses
t	n x 1 matrix, data for nonparametric part
spar	scalar smoothing parameter, as in smooth.spline
df	scalar equivalent number of degrees of freedom (trace of the smoother matrix), as in smooth.spline
family	text string, family of distributions (e.g. "gaussian" or "bernoulli", see details for glm.ll)
link	text string, link function (depending on family, see details for glm.ll)
b.start	p x 1 vector, start values for linear part
m.start	n x 1 vector, start values for nonparametric part
grid	m x q matrix, where to calculate the nonparametric function (default = t)
offset	offset
method	"speckman" or "backfit"
weights	binomial weights
weights.trim	trimming weights for fitting the linear part
weights.conv	weights for convergence criterion
max.iter	maximal number of iterations
eps.conv	convergence criterion
verbose	print additional convergence information
...	further parameters to be passed to smooth.spline

Value

List with components:

b	p x 1 vector, linear coefficients
b.cov	p x p matrix, linear coefficients
m	n x 1 vector, nonparametric function estimate
m.grid	m x 1 vector, nonparametric function estimate on grid
it	number of iterations
deviance	deviance
df.residual	approximate degrees of freedom (residuals)
aic	Akaike's information criterion

Note

This function is mainly implemented for comparison. It is not really optimized for performance, however since it is spline-based, it should be sufficiently fast. Nevertheless, there might be several possibilities to improve for speed, in particular I guess that the sorting that smooth.spline performs in every iteration is slowing down the procedure quite a bit.

Author(s)

Marlene Mueller

References

Mueller, M. (2001) Estimation and testing in generalized partial linear models – A comparative study. Statistics and Computing, 11:299–309.

Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. London: Chapman and Hall.

See Also

kgplm

Examples

  ## generate data
  n <- 1000; b <- c(1,-1); rho <- 0.7
  mm <- function(t){ 1.5*sin(pi*t) }
  x1 <- runif(n,min=-1,max=1); u  <- runif(n,min=-1,max=1)
  t  <- runif(n,min=-1,max=1); x2 <- round(mm(rho*t + (1-rho)*u))
  x  <- cbind(x1,x2)
  y  <- x %*% b + mm(t) + rnorm(n)

  ## fit partial linear model (PLM)
  k.plm <- kgplm(x,t,y,h=0.35,family="gaussian",link="identity")
  s.plm <- sgplm1(x,t,y,spar=0.95,family="gaussian",link="identity")

  o <- order(t)
  ylim <- range(c(mm(t[o]),k.plm$m,s.plm$m),na.rm=TRUE)
  plot(t[o],mm(t[o]),type="l",ylim=ylim)
  lines(t[o],k.plm$m[o], col="green")
  lines(t[o],s.plm$m[o], col="blue")
  rug(t); title("Kernel PLM vs. Spline PLM")

  ## fit partial linear probit model (GPLM)
  y <- (y>0)
  k.gplm <- kgplm(x,t,y,h=0.35,family="bernoulli",link="probit")
  s.gplm <- sgplm1(x,t,y,spar=0.95,family="bernoulli",link="probit")

  o <- order(t)
  ylim <- range(c(mm(t[o]),k.gplm$m,s.gplm$m),na.rm=TRUE)
  plot(t[o],mm(t[o]),type="l",ylim=ylim)
  lines(t[o],k.gplm$m[o], col="green")
  lines(t[o],s.gplm$m[o], col="blue")
  rug(t); title("Kernel GPLM vs. Spline GPLM (Probit)")

gplm documentation built on May 2, 2019, 2:10 a.m.