alik_inla: Log-likelihood approximation

Description

Log-likelihood approximation.

Usage

alik_inla(
  par_vals,
  formula,
  family = "gaussian",
  data,
  weights,
  subset,
  offset,
  atsample,
  corrfcn = "matern",
  np,
  betm0,
  betQ0,
  ssqdf,
  ssqsc,
  tsqdf,
  tsqsc,
  dispersion = 1,
  longlat = FALSE
)

Value

A list with components

par_vals A data frame of the parameter values.
aloglik The approximate log-likelihood at thos parameter values.

Arguments

par_vals: A data frame with the components "linkp", "phi", "omg", "kappa". The approximation will be computed at each row of the data frame.
formula: A representation of the model in the form response ~ terms.
family: The distribution of the response. Can be one of the options in .geoBayes_models or "transformed.gaussian".
data: An optional data frame containing the variables in the model.
weights: An optional vector of weights. Number of replicated samples for Gaussian and gamma, number of trials for binomial, time length for Poisson.
subset: An optional vector specifying a subset of observations to be used in the fitting process.
offset: See lm.
atsample: A formula in the form ~ x1 + x2 + ... + xd with the coordinates of the sampled locations.
corrfcn: Spatial correlation function. Can be one of the choices in .geoBayes_corrfcn.
np: The number of integration points for the spatial variance parameter sigma^2. The total number of points will be 2*np + 1.
betm0: Prior mean for beta (a vector or scalar).
betQ0: Prior standardised precision (inverse variance) matrix. Can be a scalar, vector or matrix. The first two imply a diagonal with those elements. Set this to 0 to indicate a flat improper prior.
ssqdf: Degrees of freedom for the scaled inverse chi-square prior for the partial sill parameter.
ssqsc: Scale for the scaled inverse chi-square prior for the partial sill parameter.
tsqdf: Degrees of freedom for the scaled inverse chi-square prior for the measurement error parameter.
tsqsc: Scale for the scaled inverse chi-square prior for the measurement error parameter.
dispersion: The fixed dispersion parameter.
longlat: How to compute the distance between locations. If FALSE, Euclidean distance, if TRUE Great Circle distance. See spDists.

Details

Computes and approximation to the log-likelihood for the given parameters using integrated nested Laplace approximations.

References

Evangelou, E., & Roy, V. (2019). Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling. Spatial Statistics, 29, 289-315.