covOrd {kergp} | R Documentation |
Warping-Based Covariance for an Ordinal Input
Description
Creator function for the class covOrd-class
Usage
covOrd(ordered,
k1Fun1 = k1Fun1Matern5_2,
warpFun = c("norm", "unorm", "power", "spline1", "spline2"),
cov = c("corr", "homo"),
hasGrad = TRUE, inputs = "u",
par = NULL, parLower = NULL, parUpper = NULL,
warpKnots = NULL, nWarpKnots = NULL,
label = "Ordinal kernel",
intAsChar = TRUE,
...)
Arguments
ordered |
An object coerced to |
k1Fun1 |
A function representing a 1-dimensional stationary kernel function, with no or fixed parameters. |
warpFun |
Character corresponding to an increasing warping function. See |
cov |
Character indicating whether a correlation or homoscedastic kernel is used. |
hasGrad |
Object of class |
inputs |
Character: name of the ordinal input. |
par , parLower , parUpper |
Numeric vectors containing covariance parameter values/bounds in the following order:
warping, range and variance if required ( |
warpKnots |
Numeric vector containing the knots used when a spline warping is chosen. The knots must be in [0, 1], and 0 and 1 are automatically added if not provided. The number of knots cannot be greater than the number of levels. |
nWarpKnots |
Number of knots when a spline warping is used. Ignored if |
label |
Character giving a brief description of the kernel. |
intAsChar |
Logical. If |
... |
Not used at this stage. |
Details
Covariance kernel for qualitative ordered inputs obtained by warping.
Let be an ordered factor with levels
.
Let
be a 1-dimensional stationary kernel (with no or fixed parameters),
a warping function i.e. an increasing function on the interval
and
a scale parameter. Then
is defined by:
where form a regular sequence from
to
(included).
At this stage, the possible choices are:
A distribution function (cdf) truncated to
, among the Power and Normal cdfs.
For the Normal distribution, an unnormalized version, corresponding to the restriction of the cdf on
, is also implemented (
warp = "unorm"
).An increasing spline of degree 1 (piecewise linear function) or 2. In this case,
is unnormalized. For degree 2, the implementation depends on scaling functions from DiceKriging package, which must be loaded here.
Notice that for unnormalized F
, we set to 1, in order to avoid overparameterization.
Value
An object of class covOrd-class
, inheriting from covQual-class
.
See Also
Examples
u <- ordered(1:6, labels = letters[1:6])
myCov <- covOrd(ordered = u, cov = "homo", intAsChar = FALSE)
myCov
coef(myCov) <- c(mean = 0.5, sd = 1, theta = 3, sigma2 = 2)
myCov
checkX(myCov, X = data.frame(u = c(1L, 3L)))
covMat(myCov, X = data.frame(u = c(1L, 3L)))
myCov2 <- covOrd(ordered = u, k1Fun1 = k1Fun1Cos, warpFun = "power")
coef(myCov2) <- c(pow = 1, theta = 1)
myCov2
plot(myCov2, type = "cor", method = "ellipse")
plot(myCov2, type = "warp", col = "blue", lwd = 2)
myCov3 <- covOrd(ordered = u, k1Fun1 = k1Fun1Cos, warpFun = "spline1")
coef(myCov3) <- c(rep(0.5, 2), 2, rep(0.5, 2))
myCov3
plot(myCov3, type = "cor", method = "ellipse")
plot(myCov3, type = "warp", col = "blue", lwd = 2)
str(warpPower) # details on the list describing the Power cdf
str(warpNorm) # details on the list describing the Normal cdf