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.
computeGamma1(
gamma2,
Z2start,
Z2,
U,
V,
singularVals,
ellStart,
gStart,
epsilonStart,
qStart,
y0Start,
tStart,
psiStart
)Model-averaged estimate for auxiliary regressors
from computePosterior.
Transformed design matrix of auxiliary regressors \(\bar{Z}_2\). See details.
Another transformed design matrix of auxiliary regressors \(Z_2\). See details.
Left singular vectors of \(\bar{Z}_1\) from svd.
Right singular vectors of \(\bar{Z}_1\) from svd.
Singular values of \(\bar{Z}_1\) from svd.
Vector \(\bar{\ell}\) see details.
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 huynhwalsnb;textualWALS.
Scalar \(\bar{\epsilon}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
Vector \(\bar{q}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
Vector \(\bar{y}_0\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
Scalar \(\bar{t}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
Diagonal matrix \(\bar{\Psi}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
See section "Simplification for computing \(\hat{\gamma}_{1}\)"
in the appendix of huynhwals;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 huynhwalsnb;textualWALS for details.
The argument Z2start is defined as huynhwalsnbWALS
$$ \bar{Z}_{2} := \bar{X}_{2} \bar{\Delta}_{2} \bar{\Xi}^{-1/2}, $$
and Z2 is defined as
$$ Z_{2} := X_{2} \bar{\Delta}_{2} \bar{\Xi}^{-1/2}. $$
Uses svdLSplus under-the-hood.