gamBiCopPDF {gamCopula}

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

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)