gamCopula (version 0.0-7)

gamBiCopPDF: Conditional density function of a Generalized Additive model for the copula parameter or Kendall's tau

Description

This function returns the density of a bivariate conditional copula, where either the copula parameter or the Kendall's tau is modeled as a function of the covariates.

Usage

gamBiCopPDF(object, newdata = NULL)

Arguments

object

gamBiCop-class object.

newdata

(Same as in predict.gam from the mgcv package) A matrix or data frame containing the values of the model covariates at which predictions are required, along with two columns named `"u1"` and `"u2"`. If this is not provided then the density corresponding to the original data are returned. If newdata is provided then it should contain all the variables needed for prediction: a warning is generated if not.

Value

The conditional density.

See Also

gamBiCop and gamBiCopPredict.

Examples

# NOT RUN {
require(copula)
set.seed(0)

## Simulation parameters (sample size, correlation between covariates,
## Gaussian copula family)
n <- 2e2
rho <- 0.5
fam <- 1

## A calibration surface depending on three variables
eta0 <- 1
calib.surf <- list(
  calib.quad <- function(t, Ti = 0, Tf = 1, b = 8) {
    Tm <- (Tf - Ti) / 2
    a <- -(b / 3) * (Tf^2 - 3 * Tf * Tm + 3 * Tm^2)
    return(a + b * (t - Tm)^2)
  },
  calib.sin <- function(t, Ti = 0, Tf = 1, b = 1, f = 1) {
    a <- b * (1 - 2 * Tf * pi / (f * Tf * pi +
      cos(2 * f * pi * (Tf - Ti))
      - cos(2 * f * pi * Ti)))
    return((a + b) / 2 + (b - a) * sin(2 * f * pi * (t - Ti)) / 2)
  },
  calib.exp <- function(t, Ti = 0, Tf = 1, b = 2, s = Tf / 8) {
    Tm <- (Tf - Ti) / 2
    a <- (b * s * sqrt(2 * pi) / Tf) * (pnorm(0, Tm, s) - pnorm(Tf, Tm, s))
    return(a + b * exp(-(t - Tm)^2 / (2 * s^2)))
  }
)

## 3-dimensional matrix X of covariates
covariates.distr <- mvdc(normalCopula(rho, dim = 3),
  c("unif"), list(list(min = 0, max = 1)),
  marginsIdentical = TRUE
)
X <- rMvdc(n, covariates.distr)
colnames(X) <- paste("x", 1:3, sep = "")

## U in [0,1]x[0,1] with copula parameter depending on X
U <- condBiCopSim(fam, function(x1, x2, x3) {
  eta0 + sum(mapply(function(f, x)
    f(x), calib.surf, c(x1, x2, x3)))
}, X[, 1:3], par2 = 6, return.par = TRUE)

## Merge U and X
data <- data.frame(U$data, X)
names(data) <- c(paste("u", 1:2, sep = ""), paste("x", 1:3, sep = ""))

## Model fit with penalized cubic splines (via min GCV)
basis <- c(3, 10, 10)
formula <- ~ s(x1, k = basis[1], bs = "cr") +
  s(x2, k = basis[2], bs = "cr") +
  s(x3, k = basis[3], bs = "cr")
system.time(fit <- gamBiCopFit(data, formula, fam))

## Evaluate the conditional density
gamBiCopPDF(fit$res)
# }