computeGamma1: Internal function: Compute model-averaged estimator of focus...

In WALS: Weighted-Average Least Squares Model Averaging

Internal function: Compute model-averaged estimator of focus regressors in walsNB

Description

Exploits the SVD of the design matrix of the focus regressors \bar{Z}_1, the model-averaged estimator for the auxiliary regressors \hat{\gamma}_{2} and the Sherman-Morrison-Woodbury formula for computing the model-averaged estimator of the focus regressors in walsNB.

Usage

computeGamma1(
  gamma2,
  Z2start,
  Z2,
  U,
  V,
  singularVals,
  ellStart,
  gStart,
  epsilonStart,
  qStart,
  y0Start,
  tStart,
  psiStart
)

Arguments

gamma2	Model-averaged estimate for auxiliary regressors from computePosterior.
Z2start	Transformed design matrix of auxiliary regressors \bar{Z}_2. See details.
Z2	Another transformed design matrix of auxiliary regressors Z_2. See details.
U	Left singular vectors of \bar{Z}_1 from svd.
V	Right singular vectors of \bar{Z}_1 from svd.
singularVals	Singular values of \bar{Z}_1 from svd.
ellStart	Vector \bar{\ell} see details.
gStart	Derivative of dispersion parameter \rho of NB2 with respect to \alpha = \log(\rho) evaluated at starting values of one-step ML. gStart is a scalar. See section "ML estimation" of \insertCitehuynhwalsnb;textualWALS.
epsilonStart	Scalar \bar{\epsilon}, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
qStart	Vector \bar{q}, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
y0Start	Vector \bar{y}_0, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
tStart	Scalar \bar{t}, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
psiStart	Diagonal matrix \bar{\Psi}, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.

Details

See section "Simplification for computing \hat{\gamma}_{1}" in the appendix of \insertCitehuynhwals;textualWALS for details of the implementation and for the definitions of argument ellStart.

All parameters that contain "start" feature the starting values for the one-step ML estimation of submodels. See section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for details.

The argument Z2start is defined as \insertCitehuynhwalsnbWALS

\bar{Z}_{2} := \bar{X}_{2} \bar{\Delta}_{2} \bar{\Xi}^{-1/2},

and Z2 is defined as

Z_{2} := X_{2} \bar{\Delta}_{2} \bar{\Xi}^{-1/2}.

Uses svdLSplus under-the-hood.

References

\insertAllCited

WALS documentation built on June 22, 2024, 9:42 a.m.