covOrd: Warping-Based Covariance for an Ordinal Input
In kergp: Gaussian Process Laboratory

Description Usage Arguments Details Value See Also Examples

Creator function for the class covOrd-class

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, 
       ...)

`ordered`	An object coerced to `ordered` representing an ordinal input. Only the levels and their order will be used.
`k1Fun1`	A function representing a 1-dimensional stationary kernel function, with no or fixed parameters.
`warpFun`	Character corresponding to an increasing warping function. See `warpFun`.
`cov`	Character indicating whether a correlation or homoscedastic kernel is used.
`hasGrad`	Object of class `"logical"`. If `TRUE`, both `k1Fun1` and `warpFun` must return the gradient as an attribute of the result.
`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 (`cov == "homo"`).
`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 `warpKnots` is given. `nWarpKnots` cannot be greater than the number of levels.
`label`	Character giving a brief description of the kernel.
`intAsChar`	Logical. If `TRUE` (default), an integer-valued input will be coerced into a character. Otherwise, it will be coerced into a factor.
`...`	Not used at this stage.

Covariance kernel for qualitative ordered inputs obtained by warping.

Let u be an ordered factor with levels u[1], ..., u[L]. Let k1 be a 1-dimensional stationary kernel (with no or fixed parameters), F a warping function i.e. an increasing function on the interval [0,1] and theta a scale parameter. Then k is defined by:

k(u[i], u[j]) = k1([F(z[i]) - F(z[j])]/theta)

where z[1], ..., z[L] form a regular sequence from 0 to 1 (included). At this stage, the possible choices are:

A distribution function (cdf) truncated to [0,1], among the Power and Normal cdfs.
For the Normal distribution, an unnormalized version, corresponding to the restriction of the cdf on [0,1], is also implemented (warp = "unorm").
An increasing spline of degree 1 (piecewise linear function) or 2. In this case, F 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 theta to 1, in order to avoid overparameterization.

An object of class covOrd-class, inheriting from covQual-class.

covOrd-class, warpFun

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