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robustgam (version 0.1.7)

robustgam.CV: Smoothing parameter selection by robust cross validation

Description

This function combines the robustgam with automatic smoothing parameter selection. The smoothing parameter is selected through robust cross validation criterion described in Wong, Yao and Lee (2013). The criterion is designed to be robust to outliers. This function uses grid search to find the smoothing parameter that minimizes the criterion.

Usage

robustgam.CV(X, y, family, p=3, K=30, c=1.345, show.msg=FALSE, count.lim=200, w.count.lim=50, smooth.basis="tp", wx=FALSE, sp.min=1e-7, sp.max=1e-3, len=50, show.msg.2=TRUE, ngroup=length(y), seed=12345)

Arguments

X
a vector or a matrix (each covariate form a column) of covariates
y
a vector of responses
family
A family object specifying the distribution and the link function. See glm and family.
p
order of the basis. It depends on the option of smooth.basis.
K
number of knots of the basis; dependent on the option of smooth.basis.
c
tunning parameter for Huber function; a smaller value of c corresponds to a more robust fit. It is recommended to set as 1.2 and 1.6 for binomial and poisson distribution respectively.
show.msg
If show.msg=T, progress of robustgam is displayed.
count.lim
maximum number of iterations of the whole algorithm
w.count.lim
maximum number of updates on the weight. It corresponds to zeta in Wong, Yao and Lee (2013)
smooth.basis
the specification of basis. Four choices are available: "tp" = thin plate regression spline, "cr" = cubic regression spline, "ps" = P-splines, "tr" = truncated power spline. For more details, see smooth.construct.
wx
If wx=T, robust weight on the covariates are applied. For details, see Real Data Example in Wong, Yao and Lee (2013)
sp.min
A vector of minimum values of the searching range for smoothing parameters. If only one value is specified, it will be used for all smoothing parameters.
sp.max
A vector of maximum values of the searching range for smoothing parameters. If only one value is specified, it will be used for all smoothing parameters.
len
A vector of grid sizes. If only one value is specified, it will be used for all smoothing parameters.
show.msg.2
If show.msg.2=T, progress of the grid search is displayed.
ngroup
number of group used in the cross validation. If ngroup=length(y), full cross validation is implemented. If ngroup=2, two-fold cross validation is implemented.
seed
The seed for random generator used in generating partitions.

Value

fitted.values
fitted values (of the optimum fit)
initial.fitted
the starting values of the algorithm (of the optimum fit)
beta
estimated coefficients (corresponding to the basis) (of the optimum fit)
optim.index
the index of the optimum fit
optim.index2
the index of the optimum fit in another representation:optim.ndex2=arrayInd(optim.index,len)
optim.criterion
the optimum value of robust cross validation criterion
optim.sp
the optimum value of the smoothing parameter
criteria
the values of criteria for all fits during grid search
sp
the grid of smoothing parameter
optim.fit
the robustgam fit object of the optimum fit. It is handy for applying the prediction method.

References

Raymond K. W. Wong, Fang Yao and Thomas C. M. Lee (2013) Robust Estimation for Generalized Additive Models. Journal of Graphical and Computational Statistics, to appear.

See Also

robustgam.GIC, robustgam.GIC.optim, robustgam.CV, pred.robustgam

Examples

Run this code
# load library
library(robustgam)

# test function
test.fun <- function(x, ...) {
  return(2*sin(2*pi*(1-x)^2))
}

# some setting
set.seed(1234)
true.family <- poisson()
out.prop <- 0.05
n <- 100

# generating dataset for poisson case
x <- runif(n)
x <- x[order(x)]
true.eta <- test.fun(x)
true.mu <- true.family$linkinv(test.fun(x))
y <- rpois(n, true.mu) # for poisson case

# create outlier for poisson case
out.n <- trunc(n*out.prop)
out.list <- sample(1:n, out.n, replace=FALSE)
y[out.list] <- round(y[out.list]*runif(out.n,min=3,max=5)^(sample(c(-1,1),out.n,TRUE)))

## Not run: 
# 
# # robust GAM fit
# robustfit.gic <- robustgam.CV(x, y, family=true.family, p=3, c=1.6, show.msg=FALSE,
#   count.lim=400, smooth.basis='tp',ngroup=5); robustfit <- robustfit.gic$optim.fit
# 
# 
# # ordinary GAM fit
# nonrobustfit <- gam(y~s(x, bs="tp", m=3),family=true.family) # m = p for 'tp'
# 
# # prediction
# x.new <- seq(range(x)[1], range(x)[2], len=1000)
# robustfit.new <- pred.robustgam(robustfit, data.frame(X=x.new))$predict.values
# nonrobustfit.new <- as.vector(predict.gam(nonrobustfit,data.frame(x=x.new),type="response"))
# 
# # plot
# plot(x, y)
# lines(x.new, true.family$linkinv(test.fun(x.new)), col="blue")
# lines(x.new, robustfit.new, col="red")
# lines(x.new, nonrobustfit.new, col="green")
# legend(0.6, 23, c("true mu", "robust fit", "nonrobust fit"), col=c("blue","red","green"),
#   lty=c(1,1,1))
# 
# ## End(Not run)

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