Spatial GLMM fitting, prediction, residuals and scoring

SpatialGlmmFit: maximises the Laplace approximation of the GLMM marginal likelihood (Newton for the latent mode, L-BFGS-B for \(\beta\), \(\log\sigma\) and \(\log\) range) with iid group intercepts (as lme4::glmer with nAGQ = 1) or a spatial field (Exp, Gau, Sph); returns the Gaussian approximation of the latent posterior (mode, sd, covariance). SpatialGlmmPredict: kriging of the latent mode and variance, response mean by the lognormal formula (Poisson) or 20-point Gauss-Hermite (binomial). GlmmResiduals: Pearson, deviance and randomised quantile residuals. CrpsGaussian, CrpsPoisson, CrpsSample: continuous ranked probability scores. Identical to the Python arm morie.fn.sglmm.

Usage

SpatialGlmmFit(
  y,
  X,
  family = "poisson",
  coords = NULL,
  groups = NULL,
  model = "Exp",
  trials = NULL,
  start = NULL
)

SpatialGlmmPredict(fit, X0, coords0)

GlmmResiduals(y, mu, family = "poisson", trials = 1, size = NULL, seed = 1)

CrpsGaussian(y, mu, sigma)

CrpsPoisson(y, lam)

CrpsSample(y, samples)

Arguments

y: Responses.
X: Design matrix.
family: "poisson" or "binomial" (residuals also "negbin").
coords, groups: Spatial coordinates or grouping factor.
model: Spatial correlation model.
trials: Binomial trials.
start: Starting parameters.
fit: A SpatialGlmmFit result with coords.
X0, coords0: Prediction design and coordinates.
mu: Fitted means (probabilities for binomial).
size: Negative binomial size.
seed: Philox seed.
sigma, lam, samples: Predictive parameters or samples.

Value

List or numeric vector.

References

Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. JASA 88, 9-25.

Dunn, P. K. and Smyth, G. K. (1996). Randomized quantile residuals. JCGS 5, 236-244.

Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. JASA 102, 359-378.

Examples

CrpsGaussian(0, 0, 1)
#> [1] 0.233695
GlmmResiduals(c(2, 0), c(2, 1))$pearson
#> [1]  0 -1