expand {deform}

Fitting low-rank nonstationary spatial Gaussian process models through dimension expansion

Description

Function exapnd fits a multi-dimensional dimension expansion model, where typically x and y coordinates in geographic (G-) space will be provided and then scaled and combined with new latent dimensions (that a functions of x and y) to give new coordinates in deformed (D-) space in which isotropy of a Gaussian process is optimally achieved.

Usage

expand(
  x,
  z,
  n,
  k = 10,
  lambda = rep(-1, length(k)),
  lambda0 = rep(exp(3), length(k)),
  correlation = FALSE,
  cosine = FALSE,
  trace = 0,
  z0 = NULL,
  standardise = "together"
)

Arguments

x

a 2-column matrix comprising x and y coordinates column-wise, respectively, or a list; see Details for the latter

z

a variance-covariance matrix

n

an integer number of data

k

an integer vector of ranks

lambda

specified lambda values

lambda0

initial lambda values

correlation

a logical defining whether z should be assumed to be a correlation matrix; defaults to FALSE

cosine

a logical defining whether the powered exponential covariance function should be multiplied by the cosine of scaled distances, i.e. giving a damped oscillation; defaults to FALSE

trace

an integer specifying the amount to report on optimisation (0, default, is nothing; 1 gives a bit)

z0

a scalar giving initial values (which alternate z0, -z0, z0, ... for latent dimensions

standardise

a character string that governs whether dimensions are scaled by a common ("together") or dimension-specific factor; defaults to "together"

Details

If x is a list, then it wants elements "x", "z" and "n" as described above.

Value

An object of class deform and then of class expansion

References

Bornn, L., Shaddick, G., & Zidek, J. V. (2012). Modeling nonstationary processes through dimension expansion. Journal of the American Statistical Association, 107(497), 281-289. doi:10.1080/01621459.2011.646919.

Examples

# one-dimensional expansion
data(solar)
expand(solar$x, solar$z, solar$n)
# equivalent to expand(solar)



# two-dimensional expansion with rank-8 and rank-5 dimensions
expand(solar$x, solar$z, solar$n, c(8, 5))