rr_est: Estimate the parameters of a spatial mixed effects model

In jelsema/RRSM: Methods for reduced rank spatial models

Description

Computes estimates of parameters for spatial mixed effects models using either EM algorithm or a Method of Moments estimation.

Usage

rr_em_nobeta(Y, X, S, epsilon = 1e-05, max_iter = 500, ...)

rr_est(method = "EM", em_type = "default", empirical = "cj",
  fitting = "frobenius", Y, X, S, X2 = NULL, cone = NULL, coords = NULL,
  knots = NULL, ...)

Arguments

Y	the observed data.
X	the fixed-effects design matrix.
S	the matrix of basis functions.
epsilon	the stopping condition for EM algorithms.
max_iter	for EM algorithms, the maximum number of iterations.
...	space for additional arguments to be passed to the estimation function (see especially rr_em_constrained).
method	string describing the type of parameter estimation; currently supported are Expectation-Maximization ("EM") and Method of Moments ("MOM").
em_type	string describing further specification for the EM algorithm. See details.
empirical	string identifying which empirical estimate to used for the empirical binned covariance matrix. See details.
fitting	string identifying which fitting method to use for MOM estimation. See details.
X2	for constrained EM algorithm, optional design matrix for unconstrained fixed-effects.
cone	for constrained EM algorithm, matrix of -1, 0, and 1's defining the order restriction.
coords	the matrix of observed locations.
knots	the matrix of knot locations.

Details

method is used to define a general type of estimation method. For method="EM", the supported options for em_type are:

• "default"A standard EM algorithm to estimate all model parameters.

• "nobeta"Similar to the default method, but the fixed-effects parameter is treated not estimated.

• "constrained"An EM algorithm in which the fixed effects parameter is subject to linear order constraints.

The Method of Moments (MOM, method="MOM") estimation is a two-step procedure. First, an empirical binned covariance matrix is computed (see mom_bec), and then the covariance matrix is fitted (see mom_fit. Different options for the empirical estimate can be selected using empirical. Currently the options are:

• "cj"The Cressie-Johanneson empirical binned covariance matrix.

• "robust"A robust empirical binned estimator based on the median absolute deviation.

• "dispersion"A robust empirical binned estimator based on a more efficient robust variance (computationally intensive).

• "wt_dispersion"A weighted version of the dispersion estimate (computationally intensive).

Additionally, there are multiple options for the fitting method (fitting):

• "frobenius"The covariance is fitted by minimizing the Frobenius norm.

• "robust"The covariance is fitted by minimizing a robust norm (using quantile regression).

Value

A list with elements bhat (estimate of beta), V, ssq, niter, and method.

Note

Some of the estimation functions do not estimate the fixed effects parameter (e.g., rr_em_nobeta, and several of the MOM estimation functions). In this case, bhat in the return object is NULL. In the estimation functions of RRSM, if bhat is NULL, then a GLS estimate will be computed automatically.

See Also

rr_em mom_bec mom_fit rr_universal_krige

jelsema/RRSM documentation built on May 19, 2019, 4:02 a.m.