mle_stcos {stcos}

MLE for STCOS Model

Description

MLE for STCOS Model

Usage

mle_stcos(
  z,
  v,
  H,
  S,
  K,
  init = NULL,
  optim_control = list(),
  optim_method = "L-BFGS-B"
)

Arguments

z

Vector which represents the outcome; assumed to be direct estimates from the survey.

v

Vector which represents direct variance estimates from the survey. The diagonal of the matrix \bm{V} described in the details.

H

Matrix of overlaps between source and fine-level supports.

S

Design matrix for basis decomposition.

K

Variance of the random coefficient \bm{\eta}

init

A list containing the initial values in the MCMC for sig2xi and sig2K. If not specified, we select an arbitrary initial value.

optim_control

This is passed as the control argument to optim. Note that the value fnscale is ignored if specified.

optim_method

Method to be used for likelihood maximization by optim. Default is L-BFGS-B.

Details

Maximize the likelihood of the STCOS model

f(\bm{z} \mid \bm{\mu}_B, \sigma_K^2, \sigma_\xi^2) = \textrm{N}(\bm{z} \mid \bm{H} \bm{\mu}_B, \bm{\Delta} ), \quad \bm{\Delta} = \sigma_\xi^2 \bm{I} + \bm{V} + \sigma_K^2 \bm{S} \bm{K} \bm{S}^\top,

by numerical maximization of the profile likelihood

\ell(\sigma_K^2, \sigma_\xi^2) = -\frac{N}{2} \log(2 \pi) -\frac{1}{2} \log |\bm{\Delta}| -\frac{1}{2} (\bm{z} - \bm{H} \hat{\bm{\mu}}_B)^\top \bm{\Delta}^{-1} (\bm{z} - \bm{H} \hat{\bm{\mu}}_B)

using \hat{\bm{\mu}}_B = (\bm{H}^\top \bm{\Delta}^{-1} \bm{H})^{-1} \bm{H}^\top \bm{\Delta}^{-1} \bm{z}.

Value

A list containing maximum likelihood estimates.

Examples

## Not run: 
demo = prepare_stcos_demo()
mle_out = mle_stcos(demo$z, demo$v, demo$S, demo$H, demo$K)
sig2K_hat = mle_out$sig2K_hat
sig2xi_hat = mle_out$sig2xi_hat
mu_hat = mle_out$mu_hat

## End(Not run)