sgplm1 {gplm}

Generalized partial linear model

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)")