SRE-class function

Spatial Random Effects class

This is the central class definition of the FRK package, containing the model and all other information required for estimation and prediction. class

Details

The spatial random effects (SRE) model is the model employed in Fixed Rank Kriging, and the SRE object contains all information required for estimation and prediction from spatial data. Object slots contain both other objects (for example, an object of class Basis) and matrices derived from these objects (for example, the matrix $S$) in order to facilitate computations.

Slots

• f: formula used to define the SRE object. All covariates employed need to be specified in the object BAUs
• data: the original data from which the model's parameters are estimated
• basis: object of class Basis used to construct the matrix $S$
• BAUs: object of class SpatialPolygonsDataFrame, SpatialPixelsDataFrame of STFDF that contains the Basic Areal Units (BAUs) that are used to both (i) project the data onto a common discretisation if they are point-referenced and (ii) provide a BAU-to-data relationship if the data has a spatial footprint
• S: matrix constructed by evaluating the basis functions at all the data locations (of class Matrix)
• S0: matrix constructed by evaluating the basis functions at all BAUs (of class Matrix)
• D_basis: list of distance-matrices of class Matrix, one for each basis-function resolution
• Ve: measurement-error variance-covariance matrix (typically diagonal and of class Matrix)
• Vfs: fine-scale variance-covariance matrix at the data locations (typically diagonal and of class Matrix) up to a constant of proportionality estimated using the EM algorithm
• Vfs_BAUs: fine-scale variance-covariance matrix at the BAU centroids (typically diagonal and of class Matrix) up to a constant of proportionality estimated using the EM algorithm
• Qfs_BAUs: fine-scale precision matrix at the BAU centroids (typically diagonal and of class Matrix) up to a constant of proportionality estimated using the EM algorithm
• Z: vector of observations (of class Matrix)
• Cmat: incidence matrix mapping the observations to the BAUs
• X: design matrix of covariates at all the data locations
• G: list of objects of class Matrix containing the design matrices for random effects at all the data locations
• G0: list of objects of class Matrix containing the design matrices for random effects at all BAUs
• K_type: type of prior covariance matrix of random effects. Can be "block-exponential" (correlation between effects decays as a function of distance between the basis-function centroids), "unstructured" (all elements in K are unknown and need to be estimated), or "neighbour" (a sparse precision matrix is used, whereby only neighbouring basis functions have non-zero precision matrix elements).
• mu_eta: updated expectation of the basis-function random effects (estimated)
• mu_gamma: updated expectation of the random effects (estimated)
• S_eta: updated covariance matrix of random effects (estimated)
• Q_eta: updated precision matrix of random effects (estimated)
• Khat: prior covariance matrix of random effects (estimated)
• Khat_inv: prior precision matrix of random effects (estimated)
• alphahat: fixed-effect regression coefficients (estimated)
• sigma2fshat: fine-scale variation scaling (estimated)
• sigma2gamma: random-effect variance parameters (estimated)
• fs_model: type of fine-scale variation (independent or CAR-based). Currently only "ind" is permitted
• info_fit: information on fitting (convergence etc.)
• response: A character string indicating the assumed distribution of the response variable
• link: A character string indicating the desired link function. Can be "log", "identity", "logit", "probit", "cloglog", "reciprocal", or "reciprocal-squared". Note that only sensible link-function and response-distribution combinations are permitted.
• mu_xi: updated expectation of the fine-scale random effects at all BAUs (estimated)
• Q_posterior: updated joint precision matrix of the basis function random effects and observed fine-scale random effects (estimated)
• log_likelihood: the log likelihood of the fitted model
• method: the fitting procedure used to fit the SRE model
• phi: the estimated dispersion parameter (assumed constant throughout the spatial domain)
• k_Z: vector of known size parameters at the observation support level (only applicable to binomial and negative-binomial response distributions)
• k_BAU: vector of known size parameters at the observed BAUs (only applicable to binomial and negative-binomial response distributions)
• include_fs: flag indicating whether the fine-scale variation should be included in the model
• include_gamma: flag indicating whether there are gamma random effects in the model
• normalise_wts: if TRUE, the rows of the incidence matrices $C_Z$ and $C_P$ are normalised to sum to 1, so that the mapping represents a weighted average; if false, no normalisation of the weights occurs (i.e., the mapping corresponds to a weighted sum)
• fs_by_spatial_BAU: if TRUE, then each BAU is associated with its own fine-scale variance parameter
• obsidx: indices of observed BAUs
• simple_kriging_fixed: logical indicating whether one wishes to commit to simple kriging at the fitting stage: If TRUE, model fitting is faster, but the option to conduct universal kriging at the prediction stage is removed

References

Zammit-Mangion, A. and Cressie, N. (2017). FRK: An R package for spatial and spatio-temporal prediction with large datasets. Journal of Statistical Software, 98(4), 1-48. doi:10.18637/jss.v098.i04.

See Also

SRE for details on how to construct and fit SRE models.