Description Usage Arguments Value Note Author(s) References See Also Examples

This function is a constructor for the `'corRExpwr2'`

class, representing a non-separable spatial correlation structure. Letting *rs* denote the spatial range, *ps* the spatial shape, *rt* the temporal range, *pt* the temporal shape, and *lambda* the space-time interaction, the correlation between two observations a distance *d* apart in space and *t* in time is *exp(-(d/rs)^ps - (t/rt)^pt - lambda * (d/rs)^ps * (t/rt)^pt)*.

1 2 3 | ```
corRExpwr2(value = numeric(0), form = ~ 1,
metric = c("euclidean", "maximum", "manhattan", "haversine"),
radius = 3956)
``` |

`value` |
optional numeric vector of five parameter values for the powered exponential correlation structure, corresponding to the “spatial range”, “spatial shape”, “temporal range”, “temporal shape”, and “space-time interaction”. The range parameter values must be greater than zero, the shapes in the interval (0, 2], and the interaction greater than or equal to zero. Defaults to |

`form` |
one-sided formula of the form |

`metric` |
optional character string specifying the distance metric to be used. The currently available options are |

`radius` |
radius to be used in the haversine formula for great-circle distance. Defaults to the Earth's radius of 3,956 miles. |

Object of class `'corRExpwr2'`

, inheriting from class `'corRSpatioTemporal'`

, representing a non-separable spatial correlation structure.

When `"haversine"`

is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the `form`

argument.

Brian Smith [email protected]

Cressie, N. and Huang, H.-C. (1993) “Classes of Nonseperable, Spatio-Temporal Stationary Covariance Functions”, *Journal of the American Statistical Association*, 94, 1330-1340.

Gneiting, T. (2002) “Nonseparable, stationary covariance functions for space-time data”, *Journal of the American Statistical Association*, 97, 590-600.

1 2 3 4 5 6 7 8 9 10 11 | ```
sp1 <- corRExpwr2(form = ~ x + y + t)
spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4, t=(0:4)/4)
cs1Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t)
cs1Expwr <- Initialize(cs1Expwr, spatDat)
corMatrix(cs1Expwr)
cs2Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t, metric = "man")
cs2Expwr <- Initialize(cs2Expwr, spatDat)
corMatrix(cs2Expwr)
``` |

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