GeoModels-spacetime-ordering: Ordering Conventions for Spatio-temporal Data, Covariates and...

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

Ordering Conventions for Spatio-temporal Data, Covariates and Predictions

Description

Defines the ordering used by GeoModels for fixed-location and dynamic-location spatio-temporal data, observation-level means and covariates, and kriging prediction tasks.

Details

The conventions below apply consistently to data, coordinates, design matrices, known mean vectors, and prediction outputs.

Irregular temporal coordinates

For the explicit-coordinate space-time interfaces, coordt is a numeric coordinate vector and does not need to be equally spaced. Covariance, likelihood, pair-selection, variogram, neighborhood and kriging calculations use temporal lags derived from the supplied values, typically |t_i-t_j|. Consequently, maxtime is a temporal-distance threshold expressed in the same units as coordt, not an index lag or an order of neighboring time points.

Important exceptions are explicit. Space-time GeoSimapprox(..., method = "CE") requires finite, strictly increasing, equally spaced temporal coordinates, and space-time turning-bands simulation is not implemented. GeoSimcond and GeoOutlier currently reject space-time input.

The spobj route has a separate legacy limitation: the current sp2Geo() conversion of STFDF/STIDF objects replaces their time positions by sequential indices 1, 2, ..., T. Therefore an irregular original time spacing is not preserved through spobj. When irregular temporal distances matter, pass the data and coordinates through the explicit interface and supply the numeric coordt values directly.

Fixed spatial locations

Let T be length(coordt) and let N be the number of rows of coordx. The data must be a T \times N matrix. Row t corresponds to coordt[t], and column i corresponds to row i of coordx.

The internal observation order is time-major and is equivalent to c(t(data)):

time 1: site 1, site 2, ..., site N
time 2: site 1, site 2, ..., site N
...
time T: site 1, site 2, ..., site N

Any observation-level vector, including a known mean vector, must use this order. A design matrix X must have NT rows in the same order. For example, if X_time has one row per time, X_time[rep(seq_len(T), each = N), , drop = FALSE] creates the corresponding observation-level design.

Dynamic spatial locations

For dynamic locations, coordx_dyn must be a list of length T. The element coordx_dyn[[t]] is an N_t \times 2 or N_t \times 3 matrix containing the locations observed at coordt[t].

The data must be a list of length T; data[[t]] must contain N_t values, and its i-th value corresponds to row i of coordx_dyn[[t]]. The internal order is the time-wise concatenation unlist(data, use.names = FALSE), matched by do.call(rbind, coordx_dyn):

all observations at time 1,
then all observations at time 2,
...,
then all observations at time T.

A design matrix X can be supplied either as a (\sum_t N_t) \times p matrix in this concatenated order, or as a list of length T with X[[t]] having N_t rows and the same row order as coordx_dyn[[t]]. A known observation-level mean uses the same time-wise concatenation.

Mean parameters

For a univariate linear mean,

\mu = X\beta.

The regression vector \beta is represented by the parameters mean, mean1, mean2, and so on. The columns of X correspond to these coefficients in exactly this order. An intercept-only model is equivalent to a one-column matrix of ones and the single coefficient mean. A supplied observation-level mean vector is a known mean and is not interpreted as regression coefficients.

Kriging prediction order

Let N_{loc} be the number of rows of loc and let T_{loc} be length(time). Kriging prediction tasks are ordered location-major:

location 1: time 1, time 2, ..., time Tloc
location 2: time 1, time 2, ..., time Tloc
...
location Nloc: time 1, time 2, ..., time Tloc

Therefore the rows of Xloc and the elements of Mloc must follow this order. If X_time_pred has one row per prediction time, use X_time_pred[rep(seq_len(Tloc), times = Nloc), , drop = FALSE]. Equivalently, if mu_time contains one prediction mean per time, use rep(mu_time, times = Nloc) for Mloc.

Dynamic coordinates describe the observed sites only and do not change the prediction-task order. Spatio-temporal kriging output is a T_{loc} \times N_{loc} matrix: rows correspond to time and columns correspond to rows of loc.

See Also

GeoFit, GeoSim, GeoVariogram, GeoKrig, and GeoKrigloc.

Examples

T <- 3
N <- 2
data <- matrix(seq_len(T * N), nrow = T, ncol = N)
c(t(data))

X_time <- cbind(1, seq_len(T))
X <- X_time[rep(seq_len(T), each = N), , drop = FALSE]

Nloc <- 2
Xloc <- X_time[rep(seq_len(T), times = Nloc), , drop = FALSE]
Mloc <- rep(seq_len(T), times = Nloc)

## Irregular observation times are allowed in the explicit interface.
coordt_irregular <- c(0, 0.25, 1.1, 2.8)
## Temporal lags are based on differences between these values; for example,
abs(outer(coordt_irregular, coordt_irregular, "-"))

GeoModels documentation built on Sept. 23, 2026, 5:07 p.m.