Spatial GLM, robust semivariogram, loss and weight normalisation

R arm of morie.fn.sglm, sgcrh, sglss and sgrwn. Sglm: spatial linear model by ML (Likfit) with generalised-least-squares standard errors for family = "gaussian", or the Laplace-approximation spatial GLMM (SpatialGlmmFit) for Poisson and binomial responses. Sgcrh: Cressie-Hawkins robust semivariogram, with the 0.045/N^2 term of Cressie (1993) or without it (method = "gstat"), gstat's default bins. Sglss: mean squared error loss. Sgrwn: row-standardised weights (zero rows kept).

Usage

Sglm(x, y, coords, family = "gaussian", model = "Exp")

Sgcrh(data, coords, lags = 15, cutoff = NULL, method = "cressie")

Sglss(predicted, observed)

Sgrwn(W)

Arguments

x

Design matrix (include an intercept column for an intercept).

y

Responses.

coords

Locations (n x 2, or a vector for points on a line).

family

"gaussian", "poisson" or "binomial".

model

Correlation model.

data

Observations.

lags

Number of distance bins.

cutoff

Largest distance considered.

method

"cressie" or "gstat".

predicted, observed

Predictions and observations.

W

Weights matrix.

Value

A list (the Python result's fields).

References

Cressie, N. and Hawkins, D. M. (1980). Robust estimation of the variogram: I. Mathematical Geology 12, 115-125.

Cressie, N. (1993). Statistics for Spatial Data, revised edition. Wiley.

Schabenberger, O. and Gotway, C. A. (2005). Statistical Methods for Spatial Data Analysis. Chapman and Hall/CRC.

Examples

xy <- rbind(c(0, 0), c(1, 0.2), c(2.1, 0), c(0.1, 1), c(1.2, 1.1), c(2, 0.9))
Sgcrh(c(1, 2.4, 1.3, 3.1, 1.9, 2.2), xy, lags = 3, cutoff = 2)$gamma
#> [1] 0.6936064 0.5020770
Sgrwn(rbind(c(0, 2, 2), c(1, 0, 0), c(0, 0, 0)))$W_normalized
#>      [,1] [,2] [,3]
#> [1,]    0  0.5  0.5
#> [2,]    1  0.0  0.0
#> [3,]    0  0.0  0.0